Fury has been out of action since defending his WBC heavyweight belt against Dillian Whyte earlier this year.
The Gypsy King is eyeing a return to the ring before the end of this year, and has put plans in motion to that end.
Usyk is one of a number of opponents reportedly being considered for the next fight for the Mancunian.
However, having beaten Joshua rather comfortably in Saudi Arabia late last month, the Ukrainian claimed his fellow Brit is scared to face him.
Oleksandr Usyk claimed Tyson Fury is scared to fight him
It comes after reports claimed that Joshua is set to fight Fury later this year after accepting terms for a Battle of Britain.
Usyk, 35, told his YouTube channel: “Well, if they sign the fight contract, they will punch each other for a while.
“But the thing is that everyone is expecting Usyk vs Fury for the undisputed championship which for many years hasn’t occurred in the heavyweight division…
“I will support neither of them, I won’t even watch this fight. I don’t want to.
“Okay, I’m just joking. I will go there to watch live how they will throw punches at each other.
“Honestly, I don’t think about them at all.
“Want to know what I’m really thinking about? I want to see my children, to hug and kiss them, that’s all I’m thinking about.
“Despite his toughness and how he is generally described, he is afraid.”
Bob Arum doesn’t think Eddie Hearn wants Anthony Joshua to fight Tyson Fury
Funnily enough Usyk isn’t the only one making such accusations as Fury’s US promoter Bob Arum has near enough accused his British counterpart Eddie Hearn of the exact same thing.
“We’ve been exchanging documents with Matchroom,” Arum said during an interview with BoxingScene.com’s Keith Idec. “We don’t think that Hearn wants to make that fight.
“We really don’t think he wants to make that fight. We’re giving him every opportunity to make that fight. And if we can’t make it very shortly, Fury will fight somebody else.
“We have another opponent lined up.
“I think Hearn knows, like most boxing people know, that all things being equal, that Fury will knock Joshua out, that Joshua’s very suspect now and very tentative. And he’s still a draw card, so why would you wanna cash in on your draw card? So, I don’t think he’s gonna do it.
“I think he’s just f***in’ around with the Warrens. We talk with the Warrens every day because we’re partners [on Fury], but we’re letting them carry the ball.”