Fury has been out of action since beating Wladimir Klitschko in November 2015, having pulled out of a rematch and been forced to relinquish his titles after seeing his boxing licence revoked.
However, the 28-year-old has now set his sights on a return to the ring and claims that he is still the number one heavyweight in the world amid talk of an all-British bout against Joshua.
"It was an excellent fight, very entertaining and enjoyable and I was screaming for AJ to smash him. I wonder what people would be saying today if Klitschko had done him in the sixth. I was screaming, pulling my hair out - or what little hair I've got left - because I was worried it would cost us millions!" Fury told Sky Sports News.
"He showed a lot in that fight. He showed he can get dropped and come back, which is what champions are made of. He showed he can recover from taking big shots. There's only one fight out there, the biggest fight in the world and everyone knows that. It is the heavyweights, it is me and AJ, no one else. It is the only one the world wants to see and I am here, I am the lineal champion, I am still number one in the world and everybody knows that.
"We all saw [his career] had a life and death situation against Klitschko, but Klitschko couldn't land a glove on me. Styles do make fights but I am sure I can beat AJ with one arm tied behind my back. I don't even need a warm-up if he wants this. I have been out of the ring as long as Klitschko but the difference is, I am not 41, I am 28.
"AJ did really well to come back but I am not 41 or getting old. He is just a pumped-up weightlifter but [Klitschko] couldn't land one of those of those hooks on me, at all. It is a total clash of styles, a total clash of personalities, the complete opposites.
"I would just like to congratulate AJ for getting through the nip-and-tuck, life-and-death situation, against an old man, so well done. But let's face it, I am the man, the number one in the division. There can only ever be one heavyweight, especially in our part of the world, and it's me. It definitely isn't a pumped-up heavyweight, I can tell you that."
Fury will discover whether the British Boxing Board of Control will return his licence at a hearing next week.