The Brit has not fought since he beat Carlos Takam to retain his WBA, IBF and IBO heavyweight titles.
A number of leading fighters are desperate to be Anthony Joshua’s next opponent with the likes of Tyson Fury, Joseph Parker, Deontay Wilder and Dillian Whyte all wanting a shot.
And Hearn insists that they are edging closer to confirming an opponent.
But he wants the fight to take place on a Saturday night either at the end of March or beginning of April.
“We’re getting there,” Hearn told Sky Sports.
“As AJ says, he wants the belts, he wants to be the undisputed king of the division.
“That’s the aim, and to do that he has to win two belts.
“We’re looking at March 24, March 31 and April 7 as potential dates for his next fight, with various different venues in London and Wales, even other venues and cities around Europe as well.”
Joshua has recently been involved in a Twitter slanging match with Parker.
But the Brit says he does not take the insults too seriously.
“I don’t really get involved in the whole Twitter beef too much but as I have said it does add to it,” Joshua said.
“Saying one thing is different to acting. We’ve been in touch and we’re trying to make this fight happen.
“I commend these guys [Okolie and Chamberlain] for making this fight happen because it can be difficult and that’s what we are trying to achieve – bring an amazing fight forward for the public.”