Parker (20-0, 18 KOs) defends his world title against Hughie Fury (20-0, 10 KOs) in Manchester on September 24.
Parker won the belt when it was vacated by Tyson Fury last year as the giant Brit's career was sidetracked by drugs and depression.
Tyson Fury hasn't fought since he won the WBO, IBF, IBO and WBA titles off Wladimir Klitschko in late 2015 and remains non-commital about his own fighting future.
But he's predicting big things for 22-year-old Hughie who is coming off 18 months of inactivity to step up and take on the unbeaten Parker.
"I believe this is Hughie's time. He has the breeding, the heart and the skill to beat Parker," Tyson Fury told the Belfast Telegraph as he visited the city.
"I have been alongside Hughie for a long time, we have shared many training camps together and I know that he has the qualities needed to become world champion."
Tyson Fury felt the belt was there for the taking if his cousin was good enough.
"Of course this is a 50-50 fight and it's going to take his best performance to beat Parker, but he has that kind of performance in him," he said.
"Parker has fought at a higher level, there's no doubt about that when you look at the two records. But Hughie is ready to make the step up."
Hughie's father and trainer Peter confirmed the young heavyweight had wrapped up the sparring phase of his preparations on Wednesday (NZT) and would now taper for fight night.
Parker is fine-tuning his preparations in London before transferring to Manchester next Wednesday.
Meanwhile, fellow British heavyweight Anthony Joshua confirmed he would be taking plenty of interest in the Parker-Fury clash.
"Yeah 100 per cent, it's heavyweight boxing," the man who now holds the IBF, IBO and WBA titles, told The Sportsman.
"I'm glad they are getting it on. Hughie needs it, Parker needs it. I'm looking forward to it so I will definitely be keeping an eye on it."
Joshua wouldn't be drawn into the prospect of taking on the winner as he eyed up his options, though he is keen to try to unify the division.
"There are so many fights. I've been asked about David Haye next year, Deontay Wilder (the WBC champion) next year, Parker and Fury ... I don't even know what next year holds right now, there are so many options."
Joshua hinted that Wilder was a fight that interested him.
"It's just a matter of when," he said of taking on Wilder. "When you are in the same division at the same level, it's just a matter of when's it going to happen, not if."
Joshua's next fight is a mandatory defence of his IBF title against Bulgaria's Kubrat Pulev in Cardiff on October 28.
Parker is keen to get in the ring with Joshua if he can negotiate his way past Fury.