It will be recalled that last weekend Joshua, 28, successfully defended his titles against Carlos Takam in Cardiff and either WBO champion Joseph Parker or WBC champion Deontay Wilder appear the most likely next opponents.
But Joshua’s promoter Eddie Hearn is also eyeing an all-British showdown with Fury next year.
Fury, 29, this week contacted Trump on Twitter to ask him to join his ring walk, asking the US president
who he thinks would win a bout with Joshua.
“@realDonaldTrump who do you think wins the fury vs AJ fight? You can walk me out if you want, be a part of the biggest fight ever,” he tweeted.
A number of personal issues have kept Fury on the sidelines since November 2015, when he defeated Wladimir Klitschko for the WBA, IBF and WBO heavyweight titles, and he remains without a boxing licence.
But he believes a bout with Joshua would resemble Muhammad Ali’s legendary “Rumble in the Jungle” with George Foreman in Kinshasa in 1974.
Fury posted an image of the two all-time great combatants on Instagram, along with the caption: “This is what’s to come!
“The old champ coming back to fight a man who every1 thinks will KO me, same as Ali vs Foreman the stylish Ali vs the mummy Foreman! We all know what happens in this fight!
“I know you all got me whooped, but I will not lay down or be afraid of some muscles & I have the mentality of a winner a man who has never lost a fight.”
Fury, who is still waiting for a final ruling from UK Anti-Doping on a suspended drugs ban after the hearing was adjourned in July, also laid down the gauntlet to Wilder.
“AJ & Wilder I’m coming back for you pair my mission is seek & destroy the only thing on my mind is destruction whoever gets in my way will be dealt with accordingly.
“There’s only 1 winner & that’s the fans! Let’s make the heavyweights great again, fight the best in the division.”