It was at one stage hoped that Fury and Joshua would face off in an eagerly anticipated all-British world title fight before the end of 2022.
The fighter's teams were in talks about the fight for a few weeks but they ultimately could not come to an agreement.
The self-proclaimed lineal world heavyweight champion has since signed on to fight Derek Chisora in a trilogy bout.
The two Brits will face off at The Tottenham Hotspur Stadium on December 3.
Fury recently claimed that he "needs" to fight Joshua before he hangs up his gloves.
"I don't think I can retire today because I need that Joshua fight. We have been trying to make that fight for years. It's the fight that people want to see," Fury said.
"It's the fight that I want to see as a boxing fan. I think it would be an absolute dying travesty if me and Joshua didn't fight in this era."
It did not take Fury long to contradict himself, though. A few days later, when asked about facing Joshua, he indicated that he does not fight "cowards".
"I don't fight cowards; I only fight real men," the WBC world champion insisted.
"So, to say that's a glamour fight? No way. My glamour fight was fighting the 43-0 Deontay Wilder in America."
Matchroom supremo Hearn could not prevent himself from poking fun at Fury.
Yet the promoter also suggested that he could see the champion face Joshua before Usyk in 2023.
"Two or three days ago he said he couldn't retire unless he fought AJ, and he needs that fight badly," Hearn told IFL TV.
"You're seeing now from the social media responses; people are starting to come to terms with it doesn't really make sense what he's saying. Let him go on."
Hearn added: "Maybe he fights AJ instead of Usyk. I wouldn't even be surprised.
"That fight's so big with AJ that sometimes you just get together and you make the fight instantly."