The promoter revealed that the final aspects of the contract will be ironed out in the coming days but the bout is expected to be held in Saudi Arabia and coincide with the delayed Games in Tokyo.
Hearn said: "It will depend on timings, the date we get given is when the fight takes place and the guys know it will be around the Olympics, it could be inappropriate but it is the biggest fight in boxing and the biggest moment in AJ’s career so we have to work it out.
"Both sides have accepted one specific proposal and we are finalizing that with contracts going backwards and forwards and tiny, tiny points getting ironed out.
"We haven’t finalized an exact date, July 24 is the rough date but it may leak into early August but no later than that."
Hearn says the fight will not clash with any Olympic events due to time differences and sees the fight as "bigger" than the Games.
He said: "The Olympics will be a different timezone so it’s not really in the mindset.
"I know the Olympics is a huge event but I see them very differently. I know a lot of people won’t agree with me but I personally see this as bigger than the Olympics. I just feel it is bigger than the Olympics, for Britain, because the world will stop to watch and it’s between two Brits.
"It’s impossible to schedule anything without clashing with something, it’s impossible so we will go on the date we are told to go on."