AJ lost his WBA, WBO, IBF and IBO world heavyweight titles after being beaten by Oleksandr Usyk at the Tottenham Hotspur Stadium last month.
Joshua will fight the Ukrainian for the second time in the upcoming spring and Fury offered to coach him.
"I believe that if I trained Anthony Joshua for the fight with Usyk, then he’d definitely win the fight", said the Gypsy King. "I’m offering my services to him – for me to train him for his rematch. And I guarantee he would win. I’d get him to fight like a big man."
Joshua welcomed Fury's offer to coach him and said that he is welcome to do a bit of sparring with him as well. AJ told iFL TV: "Yeah lovely mate, if he takes no money for it. I don’t know if he’s after a quid or two.
"He’s more than welcome to come through the doors, he can even spar with me as well. I need a coach that’s lived it, breathed it, so it’ll be perfect."
Joshua and Fury were in talks over a fight, which was initially scheduled to take place this August. However, it was cancelled after an arbitration judge ruled that the Gypsy King would have to take on Deontay Wilder first.
After the highly-awaited fight between the two was scrubbed, Joshua believes that a filmed sparring session would be the best way to get Fury in the ring.
"That’ll be the easiest way to get him in the ring", said AJ. "I’ll set up a camera, Eddie [Hearn] will be there with a few cameras running it on Facebook or YouTube."
Joshua also added that Fury coaching him would be an opportunity to replicate some of the icons of boxing.
He said: "I’m seeing pictures with Sugar Ray Robinson, Joe Louis, Archie Moore, Muhammad Ali, all sitting together, in each others training camps. I feel like I’ve been tucked away a lot. Come into my training camp, come and see what the heavyweight champion gets up to.
"Tyson can definitely come and watch me train, 100 per cent. Sparring ain’t fighting, so he can definitely come in, he’s more than welcome to step in to the gym and give me some tips.
"I’m not fighting him next anyway so he ain’t got nothing to worry about."
Joshua seems to have no problem with Fury coaching him for his rematch against Usyk and after how things unravelled in their first fight, the 32-year-old could do with some tips from the Gypsy King.
Besides, this would probably be the closest we'd come to seeing a fight between the two.