The Matchroom promoter revealed that he was in “advanced” talks for AJ, 35, to face The Problem Child, 28, and Hearn believes the fight will eventually happen.
Speaking to The Stomping Ground about how far along the negotiations are for the Joshua-Paul bout, Hearn said: “I never really expected this fight to happen, but the more conversations I have, the more I think there’s a very good chance it can happen.”
Hearn added he thinks Paul - who is coming off his victory over former middleweight champion Julio Cesar Chavez Jr. - is determined to get in the ring with Joshua.
The promoter said: “I believe Jake Paul wants the fight. Don’t ask me, but he believes he can win, and that’s even more dangerous.
“You can go in and think, ‘Well, if I get hurt.’ No, he’s convinced he beats Anthony Joshua.
“Be careful what you wish for because this is not what you’re used to. Respect for taking the challenge, and we’ll see if it comes off.”
Even so, Hearn insisted a fight between Paul and Joshua - the former two-time unified heavyweight champion - was a “mismatch”.
He said: “I’m not going to tell you it’s a fight of the year contender. I’m not going to tell you it’s competitive.
“I think it’s a mismatch, and I think it’ll mean that Jake Paul will leave the sport forever. Because I don’t think he’ll ever step back into the ring after he gets chinned by Anthony Joshua.
“There are a lot of people who would love to see that.”
While Hearn believes a Joshua-Paul fight would be “the biggest fight” in boxing history commercially, the promoter added that a match between AJ and Tyson Fury, 37, would be bigger for the sport itself.
He said: “Obviously, for boxing, AJ-Fury is the one, but I do understand that commercially, this is probably the biggest fight in boxing.”