The promoter, who recently severed ties with star man Carl Frampton, is known to be on the look out for a top fighter to fill the void and admitted he’d love to have Parker on board.
“It’s pretty obvious he’s one of the finest talents in the heavyweight division, if not the finest,” said McGuigan.
“He’s really coming on in leaps and bounds. I really wish I had a hold of Joseph Parker. I wish I could get my son to train him because he is a really special talent, no question about it.”
“I’m a purist and I watch all the talent in the country, in the world and obviously it starts here, watching whats 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.”
On Parker’s chances of fending off mandatory challenger Hughie Fury this weekend at Manchester Arena, McGuigan added: “I think Hughie Fury is a decent heavyweight, he does everything reasonably well, he’s got sound fundimentals.
“I think he (Hughie) 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.”
Parker claimed the championship in a twelve round win over Andy Ruiz Jr. back in December but has been forced to wait to face Fury after a failed attempt to land home advantage in May.
Fury pulled out through injury, forcing both sides to come to an alternative agreement to stage the fight on UK soil.