Unbeaten knockout merchants Joshua (21-0) and Deontay Wilder (40-0) have seemingly been on a collision course for some time, particularly since the former beat Joseph Parker to add the WBO title to his WBA and IBF belts.
Negotiations with WBC holder Wilder and his camp have appeared fractious at best, but a breakthrough appears on the horizon.
However, Joshua will likely fight WBA mandatory challenger Alexander Povetkin first, with an announcement expected before the end of the week.
"The Povetkin deal will be finalised in the next 72 hours," Hearn said. "The Wilder one is not, but we're talking every day.
"A deal will be done with Wilder in the next month but we will probably move on with a Povetkin fight before that. Wilder would be December at the earliest, probably February.
"Wilder understands he has to go where Joshua tells him to and at the moment Joshua's telling him: 'You have to come to the UK'. He's up for that, but there's a lot of things that have to be worked out."
Sorry to the kids I saw on route, I couldn't stop! pic.twitter.com/pVZqEXSfRC
— Anthony Joshua (@anthonyfjoshua) June 6, 2018
Hearn raised the possibility that Joshua could fight Wilder before Povetkin, though he insisted it is more likely the Russian will be next up for the Brit.
He added: "It's an incredibly risky fight. It might be a little bit of a mad fight to take before Wilder, but that's Joshua.
"He doesn't care. He wants a challenge; he doesn't want easy fights."
Photo by Richard Heathcote/Getty Images. Caption: Heavyweight Anthony Joshua