And Hearn admits they would be “clowns” not to get the £250m super fight on for all four major world titles.
Fury, 31, destroyed Deontay Wilder over the weekend in Las Vegas to win the WBC crown but the American has 30 days to trigger a rematch clause.
Hearn told Sky Sports: “He [Joshua] phoned me yesterday, we had a good conversation on the phone and his first thing that he said is: 'how do we make this fight happen?'
“I said to him, look firstly this hinges on Wilder.”
Joshua also has the matter of his IBF mandatory challenger Kubrat Pulev with a deal for that clash already agreed in principle.
The Bulgarian is promoted by Fury's US promoter Bob Arum so Hearn will plead with the Top Rank chief to get the mandatory challenger to step aside.
Matchroom boss Hearn is confident they can strike a deal with all involved which includes his rival promoter Frank Warren.
He said: “I promise you this fight will happen.
“If we have to fight (Kubrat) Pulev, we've got to beat Pulev, and if he has to fight Wilder, he's got to beat Wilder again.
“Both of those things will happen.
“Fury will beat Wilder again and Joshua will knock Pulev clean out, despite Bob Arum telling us very differently.
“You will get this fight. We will do everything that it takes to make this fight.
“Last time, you had us and Team Wilder and we were locking heads.
“Right now, you have two guys and two camps that genuinely want this fight, that genuinely will do everything that they can to make this fight. It is the only fight.
“When are we ever going to get the chance of two British world heavyweight champions fighting for the undisputed title against each other?
“It's never happened before it will never happen again. We'd be clowns, we'd be idiots if we didn't make this fight.
“We believe we win the fight, they believe they win the fight, so let's see it.”