The WBA and IBF champion defended his belts against Carlos Takam in Cardiff and has now set his sights on unifying the heavyweight division.
Wilder and New Zealander Joseph Parker hold the other two titles with a clash against the American now looking increasingly likely sooner rather than later.
Following his brutal knockout win over Bermane Stiverne the Bronze Bomber declared "war" on the Brit before accusing Hearn of ducking the fight.
But the Matchroom supremo has now confirmed that negotiations are underway with a fight next year firmly on the cards.
"We’re not receiving any offers, any contacts, and Deontay Wilder is doing a great job of convincing people that AJ is running from this fight," he said. "Our job to deliver, but it doesn’t happen over night. This first meeting today may go well, it may go terribly, but fans need to know we want the fight. It will happen in 2018 unquestionably.
He added: "If we offered Wilder his true value, the meeting would last two minutes. So we have to compromise between reality and fantasy."
Despite Wilder appearing to be the favoured option Hearn conceded that Parker, holder of the WBO crown, is also being considered.
"The instructions from AJ is ‘I want to be the unified champion by the end of 2018’, so that means going through Wilder and Parker," he added. "We would fight Wilder in the US. We’d love the fight in the UK. Maybe we do two of them."
Joshua had earlier posted a string of tweets taking aim at his rivals, including Tyson Fury, the last undisputed heavyweight champion of the world.
The 28-year-old's opening salvo - aimed at WBO heavyweight champion Parker - being a GIF of Kermit the Frog drinking tea. The tweet read: ".joeboxerparker Sips tea, continues to read tweets & refreshes email.. Still No Offer."
WBC heavyweight Wilder was next on Joshua's hitlist, with the Watford-born fighter posting a YouTube video of a lengthy interview during which he urged the American to set up a title fight between the two.
An accompanying tweet said: "A little word on the BronzeBomber fight. Ready & waiting for the offer." A third quick-fire tweet was aimed in the direction of an out-of-shape Fury, with Joshua tweeting: "& Tyson-Fury get fit you fat f***."