"He's really coming on in leaps and bounds. He's only a baby, he's got a really good team around him - Kevin Barry, I've known for a long time ... he knows his stuff and I think Parker is going to do great things.
"I think Hughie Fury is a decent heavyweight; he does everything reasonably well, he's got sound fundamentals. I think he could give most heavyweights trouble. But I think Parker's due for a good performance and I think he's coming over here to [Anthony] Joshua's country to make a statement.
"Joseph is a naturally big guy, he's a natural, as we say over here, a natural lump, he's physically great, he's got a lot of natural skills, head movement, feet, all his fundamentals are natural and he punches hard, he's got real determination and I like him as an individual. I think he's got a lot of fire in his belly and he wants to do well and I really believe he's going to go right to the top."
Shane McGuigan is a former trainer of David Haye, an English heavyweight on the comeback from injury who has allowed Parker to train in his gym in preparation for the Fury fight. Parker, who posed for photos with the McGuigans and Groves, travels to Manchester next week for the fight at the Manchester Arena.
Barry McGuigan holds a special place in the hearts of boxing fans in the United Kingdom for his performance in beating Eusebio Pedroza for the WBA world featherweight title at a packed Loftus Road football stadium in 1985.
Born in Clones, McGuigan, now 56, was known as the "Clones Cyclone" and fought 35 times as a professional, including an extraordinary 28 knockouts in his 32 victories.
"I'm a purist and I watch all the talent in the country, in the world and obviously it starts here, watching what's happening in the UK and Ireland.
"But when you get heavyweights that are sort of a breed of their own, he stands out for me and I know he's got a bit of criticism of late but I genuinely believe he's going to be very special," McGuigan said of Parker.
"I like what I see. I really wish I had a hold of Joseph Parker," McGuigan said of the Kiwi WBO champion.
I wish I could get my son to train him because he is a really special talent, no question about it."