The world heavyweight title fight has already been nominally agreed, but the two camps still appear far apart in the terms of the contract, with Wilder demanding a 50-50 prize money split.
Hearn's tweet revealed he is on his way to Wilder's homeland, potentially to finalise terms.
Joshua would unify the division by beating Wilder, but must face mandatory challenger Alexander Povetkin of Russia first, a bout Hearn is said to be unhappy with.
Wilder, 32, rejected Hearn's opening £15m, two-fight offer, insisting on £40million ($50m) instead.
The American called Hearn a 'disease for the sport' and threatened to back out of one the sport's most-anticipated clashes.
Joshua's fellow Brit heavyweight Tony Bellew tore into Wilder's team for the trash talk, claiming the situation was now 'an absolute mess'.
Bellew, 35, defended Hearn's offer, telling the Metro: "You can't say 'listen, I'm going to give you $50m if you sign this blank piece of paper'. That's insane, basically signing your career over.
"Anthony Joshua's whole career is worth more than $50m. I think Wilder is fooling no one, it's clear it was a publicity stunt."
Bellew also blasted Wilder's reputation, saying: "He's supposed to be the WBC heavyweight champion of the world. He's supposed to be the face of boxing in America. He's not even the face of his city.
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"No one knows him, it's a sham of a job that's been done for him on the promotional front. He should be a mega-star.
"This is a man who wears the same belt as Muhammad Ali and Mike Tyson once did, and yet nobody knows him. His country doesn't back him.
"The whole situation is an absolute mess. Wilder can come up with all the stupid things he likes, he's full of it.
"If you have $50m, then show proof of funds. Or send over the contract."
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