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'AJ' and Fury agreed to a two-fight deal in 2020 and talks are ongoing over a mega-unification clash, which could take place in either June or July.
Fury, who defeated Deontay Wilder last February in a masterclass performance, recently posted on social media a video of him going for a freezing swim in Morecambe Bay.
But the video sparked concerns with some boxing fans over the 32-year-old WBC champ's physique, despite Fury not being in a training camp for a potential Joshua fight.
Matchroom chief Eddie Hearn admitted that he was startled with Fury's weight after watching the video.
However, Joshua was on the opposite spectrum to his promoter as he insisted that he will face the "best Tyson Fury" in their all-British showdown.
Hearn told SecondsOut: "I think before he goes into any main camp he doesn't look like 'AJ,' ever.
"I said to 'AJ' the other day, 'Did you see Fury jumping in the sea? He looked like me!'
"The response from AJ was, 'We're gonna get the best Tyson Fury, so I don't care if he's carrying a bit of extra weight now, I'm training for the best-ever Tyson Fury.'
"And, make no mistake, Fury will be in top shape for this fight."
Joshua, 31, made his first title defence post-Andy Ruiz Jr II last December and sealed a stunning ninth-round KO victory over Kubrat Pulev in London.
Fury planned for a homecoming fight at the end of 2020 amid an ongoing legal dispute over the third fight with Wilder.
However, the 'Gypsy King' hasn't competed since his sensational seventh-round TKO win over Wilder in their blockbuster rematch.
Hearn has insisted that 'AJ' hasn't eased up his training and is "preparing for the fight of his life."
The 41-year-old promoter explained: "We've still probably got maybe four/five months to go. He hasn't even started camp yet.
"I think the impressive thing from both these guys is they haven't stopped training. 'AJ,' since his last fight, he don't wanna stop training.
"I even said to him, 'What about a little bit of warm weather? Go and relax a little bit? You don't wanna over-train.'
"He said, 'No, I'm fine at Finchley.' He's sparring, he's training, he's preparing for the fight of his life."
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