Fury has been out of the ring since beating former champion Wladimir Klitschko in November 2015 following concerns over his mental health and a drugs ban from the British Boxing Board of Control (BBBC).
The 28-year-old was forced to vacate his WBA and WBO titles as a result, but he is targeting a return to the sport in the wake of Joshua's thrilling 11th-round stoppage of Klitschko in front of a record 90,000 crowd at Wembley last month.
"Eddie Hearn has already booked Wembley Stadium for next April. There isn't another stadium where it should take place. I would fight Joshua in October but I believe Klitschko will take the rematch," he told The Telegraph.
"Deep down, I don't think they want to fight me yet. Joshua struggled with Klitschko. And I took Klitschko to school, toyed with him, put my hands behind my back, literally, while he was letting his cannons go, slipping out of the way of them. They are not ready for that.
"A lot of people have picked AJ to beat me, but I've said many times that we are in a sport called 'the sweet science' and it's not a bodybuilding contest or a strongman competition. Joshua is an easy fight for me."
Fury will discover this week whether his boxing licence will be restored following his admission that he took cocaine to help cope with depression, but the former champion rejected the suggestion that he is a drugs cheat.
"I've never taken a drug in my life. These people can say what they like but I'm suing them for what they have done to me. They thought they had a villain and that they were going to take me down. This went on from before the Klitschko fight. If I tested positive then why didn't they ban me then?" he added.
"To be honest I didn't want to live. If I had cheated, fine. But I have not cheated. I beat Klitschko on ability. I don't need a drug. I'm a giant already. For them to say that about me, it sent me under. I did not want to live anymore. But I feel differently now.
"I'm not annoyed that AJ has been lifted up there by some people as the number one. They were saying before that he could beat me. It is what it is. I am the outlaw of this boxing game - and I love it. I've been written off so many times. How many times was Muhammad Ali written off in his career? But come Sonny Liston, Joe Frazier, George Foreman, he beat them all. And when the time comes, I'll go through them, and all their unbeaten records will fall."