The pair have been involved in a war of words for some time now and Fury, who has confirmed he will reapply for his boxing licence, has been texting his rival to stoke up the fire even more.
Joshua is close to completing a deal to face WBO champion Joseph Parker in his next fight, with three world titles at stake in a unification clash, but there could be a spot open for the two Brits to go head-to-head after that.
Speaking about a potential match-up, Hearn revealed there is constant chatter between both parties and his camp would be more than willing to open discussions over a major heavyweight contest.
"I spoke to Tyson Fury this morning," he told Sky Sports News. "He even got in contact with Anthony Joshua at the weekend, so we're all talking. Let me tell you, that's a fight that we would sit down now and make for 2018.
"We are prepared to sit down and make that fight now with Tyson Fury and Anthony Joshua is as well, because he called me straight after Tyson was texting him the other day.
"I've already seen that he wants 60-40, Tyson Fury, which is not quite the idea that we have, but we are up for making the Tyson Fury fight.
"It won't be next, because we know what we're trying to do next. We're trying to clean up the division and win all the belts, but if it has to be the one after in the summer or have to be after that."