The WBC heavyweight champion has come out of retirement one more than one occasion since April - when he beat Dillian Whyte - and looks set to return to the ring before the end of the year.
It had been expected that Usyk, who last month retained his WBO, IBF and WBA (Super) titles with victory over Anthony Joshua last month, would face Fury in a unification fight, with a December date in mind.
But, on Friday, Usyk ruled out a return to the ring in 2022. He told the BBC: "It won't happen this year, that's for sure.
"I'm totally healthy and don't have any injuries, but I have old traumas which have resurfaced, and which need to be treated. I will need up to two months to recuperate."
Fury, speaking at the WWE's 'Clash at the Castle' in Cardiff, said his next opponent will be revealed in the coming days as he refuses to wait around for Usyk.
"All of a sudden Oleksandr Usyk has stated he does not want to fight any more - he wants to fight next year not this year," Fury told the crowd.
"I am not going to wait around for anybody and I will be announcing a fight next week."
Discussing a possible future move into WWE, Fury said he would "definitely be open to" the switch, but added: "At the moment I am a heavyweight world champion and I have lots of fights I have to take care of in the next few years."