Klitschko was the undisputed world champion for over four years until Fury earned a shock win against the Ukrainian in 2015.
Fury was unable to defend those titles amid mental health problems, but he has bounced back impressively.
The 31-year-old wants to stay at the top after regaining his WBC heavyweight belt in February with an emphatic win over Deontay Wilder, who he is due to face again once the coronavirus is subdued.
“I’ve won every single belt in boxing. From the English title to becoming the undisputed heavyweight champ of the world. All done, all finished. Considered the best, done,” Fury told Sky Sports on Tuesday.
“If I don’t box again, I’m happy, but if I do box again, then I continue to box. If we get past this thing, which hopefully we will, then we’re going to keep boxing and just keep taking on contenders.
“Klitschko did it until he was 40. A lot of the great champions are continuing, and continuing.
“I ain’t boxing for money, I ain’t boxing for fame, I ain’t boxing for a belt. I’m boxing because it keeps me mentally happy and I like to do it.”
Fury is in contention to face British rival Anthony Joshua, who holds the WBA, IBF, WBO and IBO world titles, in a 2021 bout after fulfilling his contractual obligations for a third fight with Wilder.
While Fury insists he has nothing to prove, he admitted he doesn’t want to walk away from the ring when he is still at the peak of his game.
“Nothing to prove to anybody. Not one thing to prove at all, but I box now, because I love boxing and I’ve been doing it all my life,” he said.
“Why walk away when I’m still only young?”