Fury will put his WBC crown on the line in front of 90,000 at Wembley on Saturday, April 23.
The two Brits will meet in the biggest heavyweight showdown in UK history with Fury the big favourite with the bookmakers.
Fury proved his class to retain the WBC crown in his epic trilogy clash with Deontay Wilder last October.
The 'Gypsy King' stopped the American in the 11th round, but not before he was forced to climb off the canvas twice in round four.
Fury also twice climbed off the canvas in his split draw with Wilder in December 2018. And former cruiserweight champion Bellew believes Fury is "going to have to get off the floor" again next month.
Bellew told talkSPORT: "Tyson Fury's the best heavyweight in the world right now, that cannot be disputed..
"But Dillian Whyte is a hard night for anybody. Anybody who thinks Dillian Whyte is going to be an easy fight is a fool… he's big, he's dangerous, he's brave and he can punch. All those attributes will cause problems for anyone.
'Tyson knows it too'
"And Tyson knows it too, he's no fool, but with Tyson's boxing ability, if he navigates his way through the first six, I expect him to come on strong in the second half of the fight.
"But, believe you me, I actually think he's going to have to get off the floor."
Bellew says that Whyte, whose only defeats have come against Anthony Joshua and Alexander Povetkin, will not get dragged into any mind games.
Whyte waited until the deadline to sign the contract, prompting Fury to say:
"Oh, my God! Dillian Whyte signed his contract for $8million.
"What a surprise! An absolute idiot. Should this even be a talking point? The man signed for the biggest pay day he's ever gonna get in his life.
"I'm gonna absolutely bust Dillian Whyte like a cheap water balloon, because you're useless, you big dosser. You useless sausage!"
'Really hard night's work for Fury'
But Bellew thinks that Whyte (28-2, 19 KOs) is being underestimated.
"Dillian Whyte is game as anything and he will jump all over Tyson Fury. He won't care about the showboating, the dancing around, the drop of the hand.
"He also won't get in Dillian's head… Tyson can't break Dillian's mindset. Dillian is a tough, rough, hard kid.
"I think it's a really, really good fight. I'm not saying Dillian's going to knock Tyson Fury out because that would be a stupid statement, but I will say this much, it wouldn't surprise me if he did.
"It's a really hard night's work for Tyson Fury. He might not want to admit this but he knows it," added Bellew.