Joshua laughed alongside Norton and the studio audience, but while Parker has admitted to putting on weight recently following his victory over Hughie Fury in Manchester in September, he said he would quickly lose it again in his forthcoming camp.
Parker told the Herald: "Looking the part doesn't always get the win… if he's looking at the pictures now, let's look at the pictures after the fight. There might be some good snaps of him on the ground, who knows?"
Asked what physical shape he was in, Parker responded with "circle", adding: "I know that I've taken time off and put on a bit of weight but I don't see any problems or issues. I know that I can burn it off fast and get in shape fast.
"He thinks he's got me physically – he may be big, he may be strong with all these muscles, but muscles aren't going to help you in the fight apart from power. He's not going to scare me physically - I think we've got under his skin mentally to this point, so I'm looking forward to being there and seeing how things go and what the result is.
"A lot of people are underestimating me because of my last two or three performances. Everyone's entitled to their own opinion, but it's just extra motivation for me to train harder and go out there and try to catch him clean."
The world title unification fight between Joshua and Parker, 26, is yet to be signed off, but it is likely to be sealed over the next few days. The bout is expected to be held in Cardiff on March 31.
David Higgins, Parker's promoter, has been in London for several days negotiating with Joshua's representative Eddie Hearn, and Parker was this afternoon scheduled to fly to England's capital with Duco Events' communications director Craig Stanaway.
A press conference will be held in London featuring the main protagonists if and when the contract is signed.
"I'm looking forward to getting there, hopefully getting the deal signed off, and getting face to face and seeing what he's about," Parker said.
Parker, who will be joined in London by trainer Kevin Barry, will fly to his Las Vegas base to prepare for the fight. In the unlikely event the contract is not signed, Parker will return to Auckland.
Asked if he was expecting "fireworks" at the press conference, Parker said, tongue in cheek after a campaign to highlight what he and Higgins have described as Joshua's "glass" jaw : "I haven't purchased any to take over, so… I don't know, I think I've done all the fireworks leading up to this on social media.
"I think if there are any fireworks it will be coming from him because obviously we did get under his skin and he got a bit angry. I'll just be myself and whatever comes out, comes out."
And while Parker is set to bank about $12million from the fight (not $30m as mentioned in some recent reports) – and even more in the rematch should he be successful – he said money wasn't a motivating factor.
"I've done it a few times now," he said. "The money – if you train hard and focus on what you have to do, the money comes. Everyone has their job. My promoters are focused on what they have to do and I know what I have to do – train hard, be mentally strong, be in great shape and put in a great performance. As long as I know what my focus is and what I have to do, the money side of things won't affect me.
"It's a great opportunity to make a statement. Being involved in a big fight is exciting – it's going to be a little part of history."
