The unbeaten fighters have been on a collision course for some time, particularly since Joshua defeated Joseph Parker to add the WBO strap to his WBA and IBF belts.
However, despite plenty of back-and-forth verbal sparring, a deal has yet to materialise and Hearn, Joshua's promoter, recently suggested that an agreement to fight Alexander Povetkin was close and the Wilder clash would have to wait until February 2019.
WBC champion Wilder threw a spanner into the works on Monday, though, when he tweeted to say that he had accepted an offer to fight Joshua in the United Kingdom.
And Hearn plans to put the ball back in Wilder's court by sending over paperwork to sign off on a blockbuster bout.
Speaking to Sky Sports, he said: "I spoke to AJ and [trainer] Rob McCracken this morning and obviously we saw Deontay Wilder's stuff on social media.
"It's great that he's come back to us. We made this offer about four weeks ago and I don't know if he's come back because he's heard we're close to closing the Povetkin fight or whether he wants the fight, but either way he's going to be getting a contract from us ASAP.
"It's obviously the fight we want. There is a lot of sorting out to do for this fight, but great news that in principle he seems to be on board for the idea of coming to the UK for the fight.
"We're going to be dealing with it and we're going to be making sure he gets the relevant paperwork."
Sorry to the kids I saw on route, I couldn't stop! 1 pic.twitter.com/pVZqEXSfRC
— Anthony Joshua (@anthonyfjoshua) June 6, 2018
Hearn envisages a return to Wembley for Joshua, but concedes there are still plenty of issues to sort before anything is signed off.
"We see this as a Wembley fight and we're quite limited in that respect," Hearn added.
"Obviously American TV and pay-per-view has to be considered. We've got to speak to them about what date suits them. There is a lot still to work out.
"I think Wembley is where Anthony Joshua wants it to take place. Obviously, [he had] a brilliant night against Wladimir Klitschko. It seems a natural home."