Whyte, 33, is challenging for his first world title against undefeated WBC champion Fury at Wembley Stadium on 23 April.
Fury is the overwhelming favourite heading into the fight given Whyte’s two professional defeats to Anthony Joshua and Alexander Povetkin. But Haye, who was due to fight Fury on two occasions in the past - only for injuries to prevent him from doing so - feels Whyte can produce the big shock.
Speaking to talkSPORT, he said: “I understand why he’s not getting the hype as though he’s going to go out there and do something special, but I’ve completely eradicated that knockout loss to Povetkin. I just feel that this is his opportunity to shock the world.
“You’ll get massive odds betting on Dillian Whyte. No one is really backing him whatsoever. But, you know, the type of opponent that you’d need to beat Tyson Fury, Dillian Whyte has all of those attributes. He can punch hard, he’s got cardio for days he’s got the desire and belief in himself.
“I think Whyte is going to pull up the upset. I think this is his opportunity. I think this is what he’s been waiting for. This happened at the right time for him and I think the fact that Tyson Fury’s so highly regarded by everybody, works in Dillian’s favour. So, I’m going with the unpopular underdog.”
On Thursday, Whyte broke his media silence by insisting he plans to quash the belief that it is the ‘Tyson Fury show’ at Wembley later this month.
“When these guys are trying to mug me off and treat me like this is the Tyson Fury show, they are going to get certain things corrected, so once things got corrected and we were close to getting them corrected, I am a professional so now here I am,” Whyte explained.
He said: “This is business. It is not the Tyson Fury show. Everybody says Tyson Fury this, Tyson Fury that. If Tyson Fury was the big star, he would have sold out the fights with Deontay Wilder. The fights were never sold out, so this sold out because of me and Tyson Fury.
“It is the Tyson Fury and Dillian Whyte show. We are both in the fight together, so certain things need to be done correctly. I don’t dance to no one’s tune, I am a warrior and survivor.
“We can dance together but it can’t be one-way traffic, so things needed to be sorted out, things needed to be arranged and had to get done. That is it.”