Joshua is current WBA, IBF, WBO, and IBO heavyweight champion while Fury is WBC heavyweight champion and both men are keen to square off.
'AJ' will defend his titles against Kubrat Pulev on December 12, while Fury will also defend his title aginst a top competitor.
Should they come out victorious, a battle of the Brits could be next up and Matchroom Boxing chief Eddie Hearn told Sky Sports per FightSports: "You break them up into probably May, June, and then November, December [for the rematch]. April, May, June, and then November, December.
"I think it's about where and of course they're two British heavyweight world champions, and if one of those fights at least didn't take place in the UK it would be a shame.
"I know ultimately people think it's my decision but it's really not. We will take all the offers that will come from all around the world and present them to both teams and both fighters. Ultimately, normally, the biggest offer wins."
Eddie Hearn has stated that Tyson Fury vs Anthony Joshua I is being targeted for April/May/June 2021, with Tyson Fury vs Anthony Joshua II then eyed for Nov/Dec 2021. [@SkySportsBoxing]
- Michael Benson (@MichaelBensonn) October 26, 2020
Fury was set to face longtime rival Deontay Wilder in a trilogy bout before the end of 2020, but the self-proclaimed 'Gypsy King' claims he has "moved on."
"I was looking forward to smashing Wilder again. A quick and easy fight," he told the Athletic. "But Wilder and his team were messing around with the date.
"They don't really want to fight the lineal heavyweight champion. They know how it ends. The world knows how it will end: with Wilder on his ass again."
However, Wilder's camp are still adamant that he is still more than willing to partake in a trilogy fight. Shelly Finkel, Wilder's co-manager, told ESPN: "Deontay and I would like to have the next fight, as planned, against Fury.
"We'll fight him any date, any place."
He then reaffirmed the 'Bronze Bomber's' stance in an interview with The Athletic, adding: "I spoke to Deontay [on Monday] night, all Deontay wants is to fight Fury. Any time, any place.
"He's disappointed. We'll see what happens in the next day or so."
Who do you think will win when Joshua and Fury inevitably come to blows?
Let us know in the comments.
Featured Image Credit: PA Images & iFL TV
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