Wilder was sent a contract for an April 13 clash at Wembley Stadium as the chances of an immediate collision with Joshua in 2018 faded.
Joshua chose to sign a two-fight deal with the National venue last week, leaving a rematch clause stipulated by Wilder for a UK-US bout double impossible.
With the first fight being at the 80,000 seater arena, Joshua now has the potential to agree a United States battle at the back end of 2019.
Hearn says Joshua will put pen to paper soon in order to prove to Wilder he’s fully on board with a huge undisputed unification next year.
“I’m pretty confident,” Hearn told Sky Sports News. “I think at the moment he’s throwing his toys out of the pram, and eventually we hope he’ll come to his senses.
“I spoke to Anthony yesterday and I think what we’re going to do is all the terms that were agreed by Deontay Wilder have now been put into the contract. They’ve had them now for over a month, and they haven’t done anything, so I think what we’re going to do, we’re going to sign the contract.
“Anthony Joshua says let’s sign the contract and put it in front of them, rather than them thinking that we’re bluffing for some bizarre reason, or we don’t want the fight.
“Anthony’s going to have a press conference for his next fight next week and he’ll be in America as well, and it will be good to go out there and say we’ve done all we can.
“You’ve agreed these terms, we’ve now even signed the contract, so fingers crossed, April 13 at Wembley will be Joshua against Wilder,” he added.
Wilder had verbally shaken hands on a $15m purse to travel to the UK, although has since retracted his acceptance and wants a far better portion of the pot to seal the deal.