Fury set Joshua's camp the ultimatum on Friday night, insisting if the deal cannot be done he will walk away and find another opponent for his next WBC title defence.
Television executives from BT Sport and streaming service DAZN are scheduled to meet on Monday with Joshua's team having already verbally accepted Fury's offer of a 60-40 purse split.
But Hearn told the Seconds Out YouTube channel: "There is no chance this fight will get signed by Monday. There is no need for this fight to get signed by Monday.
"If he doesn't (want to fight Joshua), and I guess he doesn't, then he'll do what he'll do and the fans might even fall for it."
Hearn said the contract sent by Fury's promoter Frank Warren was "all over the place" and while it is understood the sticking points relate to relatively minor details, Hearn is adamant his team will not be rushed.
"We have a meeting on Monday, with DAZN, with BT, with everybody, but it's going to take time," added Hearn. "If he wants to put a time frame on it of Monday then it's clear to the whole public he doesn't want the fight.
"It's not going to get signed on Monday so if he's walking away on Monday the fight's off."
Fury made the offer to Joshua on social media earlier this month after it became clear a potential bout with Ukrainian Oleksandr Usyk would not happen until the new year.
Joshua immediately accepted Fury's invitation as well as the prospective purse split, and the deal was backed up by an exchange of letters between Hearn and Fury's promoter Frank Warren.
But speaking to BT Sport on Saturday night, Fury expressed frustration with the delay and maintained he was not prepared to wait any longer for Joshua's team to seal the deal.
Speaking at ringside prior to Joe Joyce's win over Joseph Parker, Fury said: "They had had the opportunity to agree to this fight for about a month.
"They have had the contract for over a week, still not signed, still a few more excuses they are going to come back with.
"We will know more on Monday, I think. The two broadcasters are going to meet up and then we will know from there. I am sick of setting deadlines. They either want this poxy fight or they don't."