In his last fight, Fury outpointed Klitschko in Dusseldorf, flummoxing the giant Ukrainian and longtime heavyweight champion with his unorthodox movement in November of 2015.
The 28-year-old even predicts a fight with Joshua would be so one-sided, it would allow him to showboat "with one hand behind his back".
"I am the man, the number one in the division", Fury said.
Joshua, 27, stopped Klitschko in the 11th round of Saturday's Wembley super-fight to add the vacant World Boxing Association and International Boxing Organisation titles to his International Boxing Federation crown.
"I also feel that after Klitschko dropped Joshua with one punch that Eddie Hearn will never let Joshua get in the ring with me".
Before his fight with Klitschko Joshua was quoted as saying he'd like to be boxing's first billionaire fighter from the sport.
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"Styles make fights but I am sure I can beat AJ with one arm tied behind my back".
Ahead of his flight with Klitschko at Wembley Stadium, the WBA confirmed that Joshua could be granted a "special permit" not to fight the mandatory challenger if there was a "very serious" alternative.
He said his victory over Klitschko, in which he overcame a sixth-round knockdown, showed he "can knock anyone out".
The minister hailed Joshua for his humility, despite his success in boxing.
Ortiz boasts a near flawless record of 27-0-KO23 and has claimed that - despite defeat - Wladimir Klitschko managed to expose a number of weaknesses in Joshua's game that he will be able to exploit.
He told the Watord Observer: "It's brilliant - there are a lot of boys who come through the doors and everyone is proud to be Finchley boxers because they look up to him as a role model". "There can only ever be one heavyweight, especially in our part of the world, and it's me".
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