The 35-year-old Ukrainian retained his WBA, WBO, IBF and IBO heavyweight titles with a split-decision win over Anthony Joshua last month and wants to add Fury's WBC crown to his collection.
He also said he wants his final fight to be at Kyiv's Olympiyskiy Stadium.
"I can have three more fights at the very most," Usyk said in an interview posted on his YouTube page on Thursday. "It is the most realistic to be in my top form. With Fury, Canelo and a farewell fight at Olympiyskiy.
"With Canelo he said that he wanted to fight me. It would be a freak fight just for the sake of earning money.
"I only need to beat Fury and then it is time to retire for me. The unification of all the belts is much more important than just a fight or another defence.
"I want to outbox Fury and I don't want to work that much just for another defence. There is much more that I can achieve."
Since his second successive victory over Joshua, which improved his perfect pro record to 20 wins, Usyk has traded barbs with Fury, who is also unbeaten in 33 fights, recording 32 wins and one draw.
Fury, 34, is expected to face Joshua in a "Battle of Britain" title bout in December.
The 32-year-old Joshua last week said he had accepted terms to face Fury and was awaiting the champion's response.
Former champion Joshua fell to 24-3 with his latest defeat to Usyk.