"Asked for $20m to move over, joker.
"Looks like I have to [fight him] again."
Fury's promoter Eddie Hearn said he has given Fury's team until the end of the week to come up with a solution, or he'll turn to a "Plan B."
"We had a deal in place with Tyson Fury and we were told the arbitration wouldn't be an issue, that we could move on with this fight," Hearn said on Matchroom's social media channels. "They (Fury's promoters) were wrong and that's on them, that's their responsibility and their problem. We hope they can solve that problem, but we have to look after ourselves and Anthony Joshua.
"We have to maintain the position of unified world champion, and those talks will continue and we want to be in a position by the end of this week to know are we fighting Tyson Fury or are we moving forward with another option."
Hearn said Joshua could instead fight the mandatory challenger for the WBO belt, undefeated Ukrainian Oleksandr Usyk.
"I had been focusing on Plan A. The only fight was Fury and we hope it can still take place," Hearn said. "The game changed — we have to have a Plan B in place, and probably a Plan C. We have different options. The one that springs to mind is Usyk."
Fury and Wilder fought a split decision draw in December 2018, before Fury won their second fight by seventh-round stoppage last February.
Fury moved on from plans for a potential third fight with Wilder, which were complicated by an injury to the American and an absence of available television dates.
Fury announced the date and location of the fight with Joshua in a video on his Twitter account on Sunday.
- AP