Meanwhile, Joshua's promoter Eddie Hearn has revealed he would be willing to drop his IBF heavyweight crown to secure a rematch with Klitschko.
Joshua saw his burgeoning reputation elevated to superstar status last Saturday night after his thrilling 11th-round stoppage of former world champion Wladimir Klitschko in London. WBC and WBO World Champions - Deontay Wilder and Joseph Parker - have also expressed interest in the fight.
"You look at the performance of Anthony Joshua which was fearless, heroic and very, very exiting - but the difference in how they handled Klitschko was vast and Tyson was far superior". I don't want to say too much because I don't know if he wants to come back and fight me. That's what boxing is all about but most fighters just don't have that hunger.
"It was a great fight".
For Klitschko - who perhaps with an extra few punches might have finished Joshua - it could spell retirement, especially after his previous defeat more than a year ago by Britain's Tyson Fury. But man he fought well.
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Hopkins believes Klitschko still has fighting left in him and would be better served by taking on opponents of a lower grade before making his final exit from the ring.
As part of his Instagram story, Joshua also showed off his wide selection of caps as well as him working in the gym.
David Haye, Tony Bellew, Hughie Fury, Dillian Whyte and Dereck Chisora are all home-grown heavyweights who can command the kind of crowds that could convince other names in the division to more regularly fight in the UK.
"He was an amateur back then but I could see a twinkle in his eyes and he looked great". "If you're willing to take on board the advice of people at the top of their sports, you're going to understand quickly that the one common thing is that you have to work hard - all of the time". It was like that for me and it's like that now.
On the big question of who's next, Joshua told Sky he has "no problem" if Klitschko wants to trigger the rematch clause in the contract.
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