Fury and Joshua are set to go head-to-head at Cardiff's Principality Stadium on December 11th after prolonged negotiations.
The Netflix bout was announced as a joint venture between Saudi powerbroker Turki Alalshikh's The Ring and UFC president Dana White, but the collaboration is causing friction.
Joshua's promoter Eddie Hearn has been in dispute with White and is unhappy with his involvement in a potential breach of contract.
And Fury suggests Hearn's personal issues with White are leaving the fight in significant doubt.
"Anthony Joshua and Eddie Hearn are trying to pull out of this fight. They're saying they're not going to fight now," Fury said in a post on social media.
"It's mainly to do with Eddie Hearn's ego. He's making up a million different things and threatening we're not going to fight."
'The Gypsy King' added that the organisers of the event are already seeking alternative opponents if the fight falls through.
"Now you've got Turki Alalshikh finding alternative, real men who will fight at the drop of a hat. Eddie Hearn has cost us the biggest fight in boxing history."
Hearn has been at odds with White since the UFC boss' launch of Zuffa Boxing earlier this year.
He insisted White could not participate in the build-up to the bout due to existing promotional contracts.
"Dana White cannot be involved with this fight promotion," Hearn told iFL TV this week. "Netflix clearly didn't get the memo. No one talks to each other.
He added: "Then Netflix say the fight is in conjunction with Dana White. Now we have to go through that process and deal with it. It's a little bit annoying but as I've shown through the UK battle that we won, we stand by our contracts."