Usyk and Fury have been in talks to fight over the past few months, with the bout pencilled in for next month in London.
The two-weight world champion has called Fury's bluff after the Brit lowballed him with a 70-30 purse split offer.
Usyk accepted this so Fury is being backed into a corner and being made to make the fight earlier than he perhaps wanted.
The Ukrainian is arguably getting the better of the mind games at the moment and Rahman feels that Usyk will cause his rival a "host of problems" and beat 'The Gypsy King'.
"Usyk possesses a whole host of problems that Tyson don't want. He's the boxer. Tyson likes to be the boxer, the elusive guy. He likes to tire these heavyweights out," Rahman told K.O. Artist Sport.
"He's not gonna do that with Usyk. It's gonna be reverse, the opposite. He don't want those kind problems. He wants his legacy intact and I think Usyk will disrupt that.
"Usyk will out Tyson Fury, Tyson Fury."
Rahman has refused to state whether he thinks this makes Usyk the best heavyweight in the world as he "might lose to Deontay Wilder".
"I'm not saying that, I'm saying that I think he can beat Tyson Fury - but I think he might lose to Deontay Wilder," Rahman added.
"Styles make fights, and I think that a boxer is the worst style for Tyson Fury. Tyson Fury needs big broad brawlers."
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