The two fighters are in talks for an all-British blockbuster bout later this year but the Gypsy King's US representative has suggested his rival promoter doesn't want the clash to happen.
Arum told BoxingScene.com: "We’ve been exchanging documents with Matchroom.
"We don’t think that Hearn wants to make that fight. We really don’t think he wants to make that fight. We’re giving him every opportunity to make that fight. And if we can’t make it very shortly, Fury will fight somebody else. We have another opponent lined up."
Joshua has lost consecutive fights to Oleksandr Usyk and Arum thinks that Hearn is aware that AJ will suffer another loss against Fury.
He said: "I think Hearn knows, like most boxing people know, that all things being equal, that Fury will knock Joshua out.
"That Joshua’s very suspect now and very tentative. And he’s still a draw card, so why would you wanna cash in on your draw card? So, I don’t think he’s gonna do it."
Arum hopes that Fury's next fight takes place in either the UK or US as he is hugely popular on both sides of the Atlantic.
He said: "Whoever Fury fights will sell out an arena in England. And, you know, even talking to Fury himself, because he’s looking at the long picture, he wants to get exposed. He’s a big attraction in the United States. He is a huge attraction in the UK. And he wants to play on that."