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Fury decimated the Bronze Bomber to become WBC world heavyweight champion back in February in their second bout and a third was slated because of a rematch clause being inserted in the contract.
Earlier this week, the Gypsy King said he had 'moved on' after claiming Wilder and his camp made two attempts to push the date back.
"I was looking forward to smashing Wilder again. A quick and easy fight," Fury told the Athletic.
"But Wilder and his team were messing around with the date.
"They don't really want to fight the lineal heavyweight champion. They know how it ends. The world knows how it will end: with Wilder on his ass again."
His promoter in the United States, Bob Arum, has also stated that the initial clause has now expired and Fury is free to fight other opponents.
However, Wilder's camp are still adamant that he is still more than willing to partake in a trilogy fight. Shelly Finkel, Wilder's co-manager, told ESPN: "Deontay and I would like to have the next fight, as planned, against Fury.
"We'll fight him any date, any place."
He then reaffirmed Wilder's stance in an interview with The Athletic, adding: "I spoke to Deontay [on Monday] night, all Deontay wants is to fight Fury. Any time, any place.
"He's disappointed. We'll see what happens in the next day or so."
Fury is in need of an opponent for December 5, though Arum has noted there is a lack of availability at the moment. Top Rank fighters Agit Kabayel, Efe Ajagba, and Oscar Rivas have all been mentioned, while Michael Hunter has offered to fight without pay.
Anthony Joshua, who has the other three belts in the heavyweight division following his rematch triumph with Andy Ruiz, is poised to take on IBF mandatory challenger Kubrat Pulev in December.
A unification bout between Joshua and Fury would be arguably the biggest fight in British boxing history.