The Briton had the IBF belt removed after it emerged that he had signed a contract with Klitschko for a rematch. The IBF contract for the fight in November stipulated that the winner would need to face Vyacheslav Glazkov as a mandatory challenger.
Glazkov will now face the American fighter Charles Martin for the vacant strap.
Fury ended the nine-year reign of Klitschko by claiming his four versions of the world heavyweight boxing title with a huge upset victory. Fury won the bout in Dusseldorf, Germany in November on points 115-112, 115-112 and 116-111. Fury stands at 25-0 for his career.
Fury's promoter told
ESPN that his fighter would "put the belt in the bin" if he was forced to fight the Russian.
"If they force Tyson to fight Glazkov, it will not happen," Mick Hennessy said. "Glazkov means nothing, he has zero value."
After the fight, Klitschko was adamant that he would have a chance to win back his titles.
"There will be a rematch. It is still early and I have to process things but there will definitely be a rematch," he said
"I couldn't show my full potential at any time. This is what I want to change in the rematch -- and I will. Failure is not an option."
After being stripped of the IBF title, Fury remains the WBA, IBO and WBO heavyweight champion, while the WBC title is held by American Deontay Wilder.
Fury, who has an Irish traveler heritage and labels himself "The Gypsy King" on social media, is at the center of a controversy over the BBC's Sports Personality of the Year (SPOTY) award.
Following sexist remarks by the new champion after the win in Dusseldorf, more than 100,000 people have signed a petition calling for his removal from the award's shortlist. The BBC has said
that his inclusion is "not an endorsement of an individual's personal beliefs."
Fury had said: "I'm not sexist. I believe a woman's best place is in the kitchen and on her back. That's my personal belief. Making me a good cup of tea, that's what I believe."
He has also said: "Tyson Fury loves his fellow humans. He doesn't hate anybody."
He also made a disparaging remark about fellow nominee, the track and field athlete Jessica Ennis-Hill, and has criticized abortion and homosexuality -- comparing the latter to pedophilia.
The boxer is also being investigated for a hate crime
by British police for comments he made on a BBC program.