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Joshua, 30, is expected to make his next title defence against IBF mandatory challenger Kubrat Pulev before the end of 2020.
But the Brit superstar's path to a mega-unification bout with Fury could be postponed if the WBO enforces a mandatory fight with Oleksandr Usyk.
The 'Gypsy King,' who is set to complete his trilogy of fights with Deontay Wilder, has already agreed to a two-fight deal with Joshua.
Hearn has insisted that the "aim was always for Anthony Joshua to become undisputed heavyweight world champion."
And Joshua's promoter reinforced the fact that 'AJ' doesn't want to fight anyone other than Fury after the Pulev fight.
Speaking to SPORTbible ahead of Mafia: Definitive Edition's release, the Matchroom chief said: "Well, first things first, the aim when we sat down in my office here about six years ago -- whenever it was, seven years ago -- the aim was always for Anthony Joshua to become undisputed heavyweight world champion. And that's still very much the aim.
"He won't let belts dictate his career, but he definitely wants to be undisputed world champion. And the only way he can do that is by maintaining the WBO title.
"Now, if there was a way -- touch wood -- he beats Pulev in December, if there was a way to make Usyk wait until after the fight, if there was a way to pay Usyk to wait, if there was any way in which all belts could be on the line, we would rather do that.
"If that was not possible, Anthony would be prepared to drop a belt to fight Tyson Fury next. I don't think Anthony wants to fight anyone else after Pulev other than Tyson Fury, so with that respect, if we have to drop a belt to do it, we will do it.
"It's just that we would much rather... I know that when you look at the commercial interest in the fight, the commercial interest of the undisputed heavyweight world championship is much bigger than 'the heavyweight world championship with every belt on the line but one that we had to just vacate.'
"Do you get what I mean? So, I know what I'm doing commercially, but more than that it's about legacy. And you can never take the undisputed world championship away."
Hearn added that Fury shouldn't brush aside the fact that he has never been undisputed champ, saying he needs to hold them all at the same time rather than individually hold them.
The 41-year-old continued: "Tyson Fury's never been undisputed world heavyweight champion. Now he talks about, 'I've won this belt, I've won that belt, I've won every belt.'
"Yeah, but you've never owned them all at the same time. That goes down in history. We won't let it get in the way of the fight, but if we can make it happen, that would be the No 1 priority."
Eddie was talking to SPORTbible for the launch of 2K Games' new Mafia: Definitive Edition, available from today on PlayStation 4, Xbox One and PC via Steam and Epic Games Store. Mafia: Definitive Edition is a comprehensive, built-from-the-ground-up remake of the original Mafia, featuring all-new gameplay sequences and features, best-in-class cinematics, an updated script filled with rich new dialogue, expanded backstories and additional cutscenes. For more information head to: mafiagame.com/buy
Featured Image Credit: PA
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