"I went to a gym in Miami where Haye was working and right next to him you'd have some 60-year-old woman hitting a punch-bag, or an overweight guy or just a kid. And there he was, heavyweight champion of the world. He had everything he needed, but it was very grounding to see the mix of people around.
"Everything in tennis is so neat and nice but boxing has sport down to its essence; it is very pure and I like that.
"I've never fought. I've put on gloves, hit the speed bag, the heavy bag, but I've never had a go. I talk about it all the time, with the guys that I work with. It would be great to get the gear on, get in a ring and do it, create our own fight club."
So why such a passionate connection with another sport? Murray thinks. "Like tennis, if you are prepared to sacrifice just a little more than your opponent, it will give you an advantage," he says. "If you've done the extra mile, you might have the better of him.
That is so important because you can prepare for a match and you think you know your opponent well, but then he comes out and does something completely different."
The 2011 season is nearing a conclusion, but Murray's plan is to be quickly out of his corner to dominate the ring in 2012. His loss to Tomas Berdych in Paris was a disappointment, but it followed a run of 18 straight match and three tournament victories, and the points differential on the day was only 122-119 in favour of the Czech.
On Sunday, the ATP World Tour Finals start in London and Murray hopes to end his campaign on a high. He is in, arguably, the best form of his career, and has overtaken Roger Federer in the world rankings, moving up to No 3.
"Getting from 20 to five seems a bigger step than four to three, but the closer you are to top spot, the bigger the leap," Murray says. "It felt huge to move up this year because I knew it was such a significant improvement. It will be different the next time I get into a Grand Slam final.
"After the US Open I sat down with the guys in my team and said now is the time to be totally serious, totally focused, because I've never felt closer to making that breakthrough. In tennis, it is not the opponent you fear, it is the failure itself, knowing how near you were but just out of reach. I think I will be able to control my emotions better next time I am in that position; I feel mentally stronger, I feel comfortable. I am as high about my game now as I was low after the Australian Open this year. This is where I want to be and I've got to keep it up."
A straight sets defeat by Novak Djokovic in Melbourne - Murray has never won a set in any of his three Slam finals Ñ took a greater mental toll than anticipated. Murray fell into a slump lasting several months and spent a lot of time evaluating his game.
"I don't think a defeat has ever taken longer to get out of my system," he admits. "The Australian Open takes place in January, so in December I decamped to Miami to prepare. I spent Christmas Day alone, running on the beach.
"It could be worse, I know, but everyone else is with their family, and all you keep thinking is, "Don't worry, it's all going to be worthwhile."
"So to get so close and lose hits you doubly hard, because of all you've given up. All that effort for not quite. Then everyone wants to console you, which is the last thing you need. You really don't want to be hear, "You're doing great and it's going to happen if you keep working hard" because you're thinking, 'Look, I am working hard, and it hasn't happened, so don't keep telling me that.' There are moments when you don't want pepping up, you don't even want to speak to people. There is nobody who can help. You are the only one who can deal with it. By March, I simply felt terrible. I hated practising. Everything was wrong.
"On your own, you can get very intense. You ask what you need to do: is it my training, my team, my preparation? In reality, it is never usually the drastic stuff. It is more about having confidence in what you are doing: coaching, tactics, the physical side. As you get older or smarter you learn to understand what is going well and how to repeat that, with maybe an extra five per cent added."
The extra, he hopes, will come in the form of Darren Cahill, the Australian coach of Murray's tennis idol Andre Agassi, whom he wishes to parachute in to up the ante around the Grand Slams. For the most part, Murray will be coached by his best friend Dani Vallverdu, a Venezuelan former Davis Cup player he met while at the academy in Spain a decade ago. Vallverdu understands him and Murray hopes Cahill will then make an added impact, the way a boxer might call on the experience of a man like trainer Emanuel Steward at an important point in his career. A full-time position is considered out of the question with Cahill based in Las Vegas and employed by ESPN.
"It is difficult but we'll find a way that works," Murray confirms. "I wanted someone who understands me, and my game - not just anybody, a big name for the sake of it."
He is a singular thinker, Murray, and some then perceive him as dour or miserable. He isn't. He can be intense about his sport, obsessive even, but he is approachable and accommodating and laughs easily. The exceptional nature of his journey is often unappreciated, too. He talks of formative years on the junior circuit when he and older brother Jamie would be the only Scottish presence in tournaments dominated by up-and-coming English players.
"Every competition seemed to take place about six hours from where we lived," he says, "but I think that was what made me an individual. We were outsiders all the time, so we became our own little team. There was nothing in Scotland. No tournaments and no players. That is very unusual in tennis, to have someone come through from a country without pedigree. I had Tim Henman to look up to, and that definitely helped, but nobody with my background."
Perhaps this was why, at 15, Murray rejected the chance to attend the British tennis academy at Sutton in Greater London and went instead to Spain, where he spent two weeks as a lonely presence in the communal dining room until befriended by Vallverdu. It has left him with an uncompromising, almost brutal, attitude to the shallow pool of talent in British tennis.
"Do you know that in Spain, at 18, your funding stops?" he asks, pointedly. "From there, you get nothing that you cannot earn for yourself. We're funding guys to 27, 28 - while in the most successful tennis nation in the world you're basically on your own. Maybe there's something in that. My mum has just come back from Russia, looking at the National Tennis Centre that has produced this great run of players, six in the top 30 women at the moment. So what great set-up do they have? Sixteen tennis courts and that's it. Not even particularly good ones, she said.
"Yet you look at the people Russia's centre has churned out and they are pretty much taking over the women's game. There is nothing about the place, really. So it is not down to facilities, either. It is about having drive and dedication and a designated formula for success.
"When I went to Spain, from the best players to the worst players we were all taught the same way, all given the same drills. They had a structure and they stuck to it.
"Go to our national centre and you've got 10 different nationalities all coaching a different way. If we don't get the results straight away, we panic and change direction. There is no confidence in our technique, no sense of sticking to an idea, no identity, no consistency in the way we teach tennis, so naturally there is no British style.
"We'll get lucky every now and then and one might get through, but there is no form to our teaching, year after year, which is why we have no depth. To be among the best tennis-playing nations you must have identity.
"When you draw a Spanish player or a South American in a tournament you know what to expect. They have a style. That is how they are taught. The Americans are all big serve, big forehand, the French are free spirits - all of their players have flair, it's a lot like their rugby team. In Britain, we get too much too young and maybe we stay attached too long. None of the other countries do it as we do and they are producing a lot more world-class tennis players than we are."
Murray is acutely aware of his lone furrow every time he arrives in a new city to play.
"We're not like Spain," he explains. "We don't have six guys in the top 30, and you notice that when there is this big crowd of French or Spanish players, and you're sat in the corner on your own. There are some good British doubles players now, so it is better than it was, but it used to feel very lonely. It's one of the reasons I like to have friends around."
Those who see Murray only as this brooding, solitary presence, all Celtic gloom and introspection, are wrong. He dipped after Melbourne but is in a happy place right now. Happy with his form and prospects. The quest for self-improvement continues and he is realistic enough to know the challenge to claim even a single Grand Slam in a golden era for men's tennis is immense. Yet Murray is not greatly given to pessimism or to beating himself up over circumstances of birth.
"This year has been good for me," he says. "I haven't won a Grand Slam but it has been my best year in all competitions and the first step is to be at ease with yourself and your progress. I understand how strong men's tennis is right now. I think I am competing against the two best players in the history of the sport in Federer and Rafa Nadal, and Djokovic has had one of the greatest individual seasons of all time.
"People pity me for being around in this era, but I believe it has made me a better player, because each year the bar is raised. It's like being Real Madrid or Manchester United behind Barcelona. Maybe the teams that come second won't be remembered, but what can they do but try their hardest? There is more to it than just winning a Grand Slam. Yes, if I didn't get there I am sure I would be very disappointed but it's not like I'm losing to bad players. It's frustrating that people might not acknowledge how close I am, but I still think I will get there.
"There will always be matches when you feel, 'I could have done better' but I don't think I've had a season in the last five when I haven't looked back knowing I've given it everything. I'd love everyone to see the work that goes into it, because this is not just a case of having talent and believing that is all it takes. I am trying so hard to get that edge.
"I suppose what spurs you on is seeing Djokovic and the difference that can be made at the top level by a very small improvement. You can go five or six tournaments without losing, but who would have expected it from him this time last year? People doubted him and now heÕs playing some of the best tennis we have ever seen."
Those on-court meltdowns, the moments of greatest pressure when Murray seems at war with himself, or his colleagues, friends and family in the players' box, are something he is making a serious effort to address, too, even if his loss of temper in Paris suggests a work in progress.
"Tennis is an individual sport and I am quite a self-conscious person," Murray admits. "There are 50,000 people watching, millions more at home, cameras everywhere and when something is happening that I don't like, or things are not going well, I have always looked up to see the people who are there for me, who aren't judging or criticising me and I direct my frustration at them.
"Anyone who has played the game knows what it is like to be under pressure and become frustrated. So, yes, I know I have to concentrate more on me, and on my own game, to become better. All I would say is that a lot of the British ex-players who commentate have never experienced that particular type of stress on court, because they were never at the level where it was present. They don't understand what it is like. It is something I need to improve on - but it isn't what will take me from No 4 to No 1. It's one thing, but there are many factors that are more important.
"I'm not perfect, I know that. But everybody is different. Roger Federer stays calm. Yet if you look at a great footballer like Wayne Rooney, getting p****d off at his team-mates or at himself, he is a completely different character but still a fantastic sportsman. I'm sure he tries to improve his temperament but, obviously, it is a part of his game that needs work. It is a flaw, but it doesn't stop Rooney being one of the best in the world.
"That is where I am. It just wouldn't make me feel good to bottle my emotions. Saying nothing and standing there makes me feel uncomfortable and flat. There is a fear of emotion in tennis. If someone boos everyone looks at them as if to ask, 'What the hell are you doing?' Yet in other sports it happens all the time.
"I find it strange that at Wimbledon every year, almost every day I get asked about the stress and pressure of playing in front of a home crowd. In every other sport, the home team is thought to have the advantage. So why should it be a problem for me? I've never felt it, never made it an excuse, and it's not going to go away, so deal with it.
"I think we as a nation expect to win and when we don't we look for these big reasons. Why did Tim Henman not win Wimbledon? Why has Andy Murray not won Wimbledon? Well, sometimes you're not quite good enough. I can't say exactly why it hasn't happened for me there, but I'll tell you what isn't the reason: the pressure of the people and the pressure of the media."
And that is what makes Murray a British sportsman to be cherished. He is very good at his job, doesn't make excuses and never stops working. And now his dinner has arrived. Poached salmon with boiled potatoes and what looks like a rice-based biscuit.
Talking football in an animated fashion Ñ he is second in a fantasy football league, although his defence may need an overhaul Ñ he is happy to extend our conversation by consuming the snack before the main course. Instantly, he is advised that the dietician wants the biscuit to be eaten after dinner, not before. Murray obliges, obediently.
Who knows if a hundred such menial repetitions, inconveniences and sacrifices might one day give him the edge to land the knockout blow in a Grand Slam final?
The frustrated pugilist within Murray will never allow him to die wondering.
- DAILY MAIL