The Matchroom promoter is keen to put on a fight between the two British former heavyweight world champions this year but plans to give the Gypsy King time to lick his wounds after his rematch loss to Oleksandr Usyk last month before making an approach.
Hearn told The Stomping Ground: "It’s literally the fight that every casual fan in the UK wants. It’s the biggest fight in boxing commercially, and when people say it’s not... Tell me a bigger fight; there isn’t one.
"I don’t know if it’s gonna happen, there’s been no discussions. Fury’s just coming off that defeat, and at some point after his break, he’s gonna turn around and decide what he wants to do. If he wants to fight AJ, the fight happens immediately. We’ll see.
"I don’t think it’s the time to start prodding Tyson Fury. Don’t forget, he lost on 21 December, so give him a few weeks [to] chill out.
"Obviously you’ve got (Daniel) Dubois fighting (Joseph) Parker on 22 February, but sooner or later in the coming weeks, we will want to put a plan together for Anthony Joshua.
"That is when the conversation will come with Frank Warren [Fury’s promoter], Spencer Brown [Fury’s manager] and His Excellency [Saudi adviser Turki Al-Sheikh]. And we’ll say: ‘Look, we want to make AJ-Fury, what do you think?’"
Hearn says Joshua knows the importance of a fight against Fury, even though it might prevent his charge from becoming world champion for a third time.
He explained: "AJ wants to become world heavyweight champion again, no doubt. He really wants to rematch Dubois, but he also understands the size of the Fury fight."