Briton Joshua, 30, defeated Mexican-American Andy Ruiz Jr in a December rematch in Saudi Arabia to win back his IBF, WBA, WBO and IBO titles.
Reports in British media say Joshua is close to agreeing a deal to face Bulgarian Kubrat Pulev, the IBF’s mandatory challenger.
“He (Joshua) wants to fight in London in June. We’re on the verge of making that happen now,” Hearn told Sky Sports. “Spurs is the front-runner and that’s what he’s asked me to do. We’ll be delivering that for him.
“We’ve had offers in from the Far East, Middle East, Africa, America, Turkey.
“He’s made it very clear to me, ‘I want to come home. I want to box in London next. I’ve been to Madison Square Garden, I’ve been to Saudi Arabia, bring me home. Forget the other offers.'”
Pulev said he was ready to “bust up” the world heavyweight champion in front of his fans in the British capital.
“Calm down champ, I see that you are very worried to fight away from home and you are absolutely right to be, haha!,” the 38-year-old Pulev said on his website.
“But rest assured, if necessary I’m ready to come to London and bust you up in front of your own fans!”
Known as The Cobra, Pulev previously challenged for the IBF world heavyweight title in 2014, losing to Wladimir Klitschko in Hamburg on a fifth-round knockout.
(Reporting by Shrivathsa Sridhar in Bengaluru and Angel Krasimirov in Sofia; Editing by Peter Rutherford and Toby Chopra)