The two heavyweights fought twice before Haye’s retirement in June, with the Bomber winning both bouts via TKO.
Both men form part of the Sky Sports punditry team on Saturday night as Whyte takes on Parker in a heavyweight match-up which could seal the winner a title shot.
But their disagreements don’t appear to have been left in the ring.
I am sticking with Whyte – although I think he might have to get off the floor
In predicting the winner of the box-office bout, Bellew told Sky Sports: “I was solid on Whyte all the way through the week and I have changed my mind at the last minute in the past, but I am sticking with Whyte – although I think he might have to get off the floor.
“He is not getting through this without getting nailed hard and everybody is overlooking Parker’s punching power.
“But Dillian has a lot going for him, he is vastly improved and seems to be thinking about the attacks these days. No, he’s not in with a big, dozy, brute like Lucas Browne this time and Parker has wins against the better fighters, but I am sticking to Whyte on points.”
In contrast, Haye is backing Parker to return to winning ways after his maiden career loss to Anthony Joshua in March.
“I see Parker potentially having problems with Whyte’s jab for the first five or six rounds, but if Parker can stay disciplined and can keep educated pressure on Whyte, I believe Parker’s engine is superior,” Haye said.
“I have never seen Whyte fight at any type of pace. He chooses to slow the pace down, he chooses to stay behind the jab and get a breather.
“With Parker, I’ve seen in the past, he has fought at a lot higher pace. He’s a younger guy, he’s the more naturally-gifted athlete. AJ wasn’t able to take him out. He’s got the youth.
“As far as I’m aware, he hasn’t been knocked out in sparring, or in a fight, or knocked down. If it gets rough, if it gets tough, my money goes on the guy who’s got the bigger punch, and the better chin. I would put my money on Parker via points decision or a late stoppage.”