Fury, 28, has dealt with depression and lost his boxing licence since beating Wladimir Klitschko in November 2015.
In a wide-ranging interview, Fury said he will shed eight stone in weight and remove the "fraud from the division".
"Joshua is a big man with a puncher's chance and has no footwork, no speed or stamina," Fury told BBC 5 live boxing.
"He is what you call a boxer's dream. I've had 18 months out and ballooned up to 26 stone. I could come back with no comeback fights and still box rings around that body builder.
'Hands behind my back'
Fury says he will be back fighting in July, on the undercard of a show at London's Copper Box Arena, if his licence is reinstated by the British Boxing Board of Control.
The BBBofC removed the fighter's licence in October 2016 eight days after he admitted taking cocaine to help him deal with depression.
The sport's British governing body says it would need a "full consultant's report" in considering their position, but the 28-year-old's camp is confident the matter will be worked out.
Fury, who refers to himself as the 'Gypsy King', also faces a UK Anti-Doping hearing on Monday relating to a failed test in June of last year.
He insists he is not "desperate" to return to the sport but wants to meet Joshua, who beat Klitschko on Saturday to unify the IBF and WBA titles before immediately referencing a future bout with Fury.
Fury has sparred with Joshua in the past and added: "I always said Wladimir would be my easiest fight. Now I change the goal posts, AJ will be my easiest fight.
"I've never been more confident or serious when I say something, I will play with Joshua like a cat with a ball of wool - hands behind my back, making a right mug of him.
"We are in the business of sweet science. Sweet science does not consist of a body beautiful, iron pumping big fella. It's feinting, jabbing, moving, gliding around the ring, that's the sweet science."
'I am the outlaw'
Fury believes he will take at least eight months to return to 18-and-a-half stone - roughly a stone heavier than he weighed in at prior to his shock win over Klitschko - and is currently in Marbella training.
He said he "enjoyed every minute" of the Joshua-Klitschko Wembley Stadium fight, but admitted concern, stating "silly things" Joshua did could have led to a defeat which would have "cost us millions" in scuppering the chances of a future match-up.
Undefeated Fury also believes the result underlines the lack of credit he received for toppling Klitschko to land three of the four heavyweight titles at the same age as Joshua - 27.
He added: "Joshua was supposed to walk right through him as he was old and useless supposedly, but it didn't work like that did it? Klitschko's been out of the ring 18 months and had a 50-50 fight with a so-called killer. I will rip the fraud from the division.
"You get two types of people in boxing, the outlaw and the Mr Nice. I am the outlaw so people love to hate me. That's my personality, love me or hate me you still have to watch me, it works. I've been through depression, life and death positions, and turned it all around."