Anthony Joshua is "talking to opponents" but time is running out for a last-gasp fight in 2025 to be organised.
Joshua has been out of the ring for almost 14 months since he was stunned with a fifth-round stoppage by fellow British heavyweight Daniel Dubois last September.
It halted Joshua's momentum under trainer Ben Davison and his charge towards another world title tilt, but Hearn revealed at the grand arrivals of Chris Eubank Jr vs Conor Benn II that a tune-up fight is on the cards and could even take place before the year is out.
"We've already got opponents that we've been talking to about a run out fight," promoter Hearn said.
"But the whole point is to not have to come and do [media obligations] and not have to just chill out, turn up on Wednesday or Thursday, weigh in, wrap your hands and go and fight.
"And it's got nothing to do with, obviously, the financials. It's just to do with getting back into the groove of fighting.
"Because every time he fights, [Joshua] has to go to a stadium and fight in front of 60,000 people in a tough fight. It's almost like just go out and just give me one to get back."
Hearn set a deadline: "We will make a decision this week on Anthony's next fight."
A fight against YouTuber-turned-boxer Jake Paul has been remarkably touted.
Paul previously told ESPN: "People are telling me to fight someone my own size. OK, how about I fight somebody who is bigger than me? His size makes him a tougher challenge than [Terence] Crawford. That's the most dangerous fight for me right now."
Although Hearn is receptive to entertaining a fight against Paul, there is no offer on the table.
"No, we've had some discussions," he confirmed.
"If we were to have a run out, a run out against Jake Paul would be quite pleasant.
"I'm not sure [Paul] is that mad. He might be, but nothing major to report at this stage. But I know they're going to make a decision themselves about what they're going to do. Hearn insisted that if Joshua does step into the ring for a low-key tune-up in 2025, it won't be against a high-profile opponent.
"If he fights this year, you probably won't even hear about it unless it's Jake Paul," he said.
Joshua's defeat to Dubois ended a run of four straight wins after back-to-back losses to Oleksandr Usyk.
With old rival Tyson Fury expected to resume his boxing career in 2026, an eagerly-anticipated bout with Joshua is still a possibility for the duo.