Britain's Joshua beat Andy Ruiz Jr in Saudi Arabia last year to regain the WBA, IBF and WBO titles.
Ruiz says pressure all on Joshua ahead of Saudi rematch
Now the 30-year-old is set to fight Bulgarian Kubrat Pulev, the IBF mandatory challenger, in June at the north London home of Premier League club Tottenham.
The plush 62,000-capacity stadium, which opened last April, is believed to have beaten competition from venues including Twickenham and Arsenal's Emirates Stadium.
"We're very close. I had a meeting with AJ last night. We've had offers in from the Far East, Middle East, Africa, America, Turkey," Hearn told Sky Sports.
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"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! Bring me home!'
"He wants to fight in London in June. We're on the verge of making that happen now. Spurs is the front runner and that's what he's asked me to do. We'll be delivering that for him."
Joshua was last in action in London back in September 2018 when he beat Alexander Povetkin at Wembley Stadium.
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