Otto Wallin's promoter has called for a rescheduling amid reports of Dillian Whyte withdrawing from their fight due to injury.
Whyte is scheduled to defend his WBC interim heavyweight title, and his status as the mandatory challenger to Fury, on October 30 against Wallin.
His reported withdrawal leaves no obvious next opponent for Fury, who stands atop the division as WBC champion after another scintillating win over Deontay Wilder.
The WBC had ruled that the winner of Fury and Wilder's trilogy fight would have 30 days to agree a fight against IBF, WBA and WBO champion Oleksandr Usyk, or would be ordered to face the reigning interim champion (the winner of Whyte vs Wallin).
But Anthony Joshua has triggered a rematch clause to ensure he fights Usyk again in early-2022.
Whyte, even if he officially withdraws from fighting Wallin, remains the interim champion.
"It's very disappointing," Wallin's promoter Dmitriy Salita told Sky Sports.
"If it is an injury, then he should heal, and they should reschedule this event. That would be the fair thing to do.
"It would not be fair to the sport of boxing for Dillian Whyte to have an injury, whatever it is, and as a result of that, to be able to be mandated to fight Fury.
"Otto is ready to go to the UK today. He had a complete training camp and this fight guarantees a lot of attention and it was truly the right eliminator for the fight with Fury.
"The fight has to be rescheduled for a later date and the winner of that fight should fight Tyson Fury. Anything else would be unfair to the sport of boxing, and unfair to Otto Wallin.
"We're definitely going to petition the WBC to make a decision.
"That's what should be decided - the winner of Whyte-Wallin fights Tyson Fury.
"The WBC will pass what I feel is an important decision, which should set things right."
Whyte had been hoping that a victory over Wallin would finally solidify him a long-awaited title opportunity. He had previously told Sky Sports: "Hopefully now the WBC forces my position and Fury has no choice.
"I am looking to fight Fury next if everything goes according to plan."
Swedish southpaw Wallin was aiming to upset Whyte and inherit his status as mandatory challenger to Fury.
Wallin gave Fury a fright when they previously fought in 2019 by inflicting a massive cut.
Wallin's promoter Salita previously said: "Out of all the great fighters that Tyson Fury beat, the one fighter that gave him most trouble, caused most controversy with the cut, who landed more punches than Wladimir Klitschko and Deontay Wilder in their first fights combined, is Otto Wallin."
Whyte previously said: "Wallin is a dangerous operator - he pushed Fury all the way."
Sky Sports Boxing schedule
October 24 - Top Rank in Atlanta
Jamel Herring vs Shakur Stevenson - WBO super-featherweight title
October 31 - Top Rank in New York
Jose Zepeda vs Josue Vargas
November 6 - Top Rank in Las Vegas
Mikaela Mayer vs Maiva Hamadouche - IBF and WBO super-featherweight titles
November 6 - BOXXER in Liverpool
November 20 - BOXXER in London
Richard Riakporhe vs Olanrewaju Durodola
Caroline Dubois professional debut
November 20 - Top Rank in Las Vegas
Terence Crawford vs Shawn Porter - WBO welterweight title
December 11 - BOXXER
Claressa Shields vs Ema Kozin
December 11 - Top Rank in Las Vegas
Vasiliy Lomachenko vs Richard Commey
December 17 - Top Rank in Montreal
Artur Beterbiev vs Marcus Browne - IBF and WBC light-heavyweight titles
December 18 - Top Rank in Glasgow
Josh Taylor vs Jack Catterall - undisputed super-lightweight title