Joshua first aims to regain his IBF, WBA and WBO heavyweight titles from Andy Ruiz Jr. in a December 7 rematch in Saudi Arabia, Sky Sports reported.
But asked what his ideal fight would be, he said, "I always change it, but right now, I'd say Fury at Wembley. The best of Britain. It is a massive fight."
Asked how likely that would be to happening, Joshua told his fans, "You will [see it]."
Fury is hoping to rematch WBC champion Wilder in February, having survived a nasty cut to stay unbeaten against Otto Wallin earlier this month. Wilder and Fury drew a fight last December.
Asked if he would eventually fight Fury and Wilder, Joshua said, "Yes, 100 percent. That's like asking if a certain football team will play another football team. Of course.
"We're in the same division, in the same era. We have to fight each other.
"We're all big draws in the heavyweight division so it would be massive.
"I'd love to fight Wilder, I'd love to fight Fury. I'm fighting Ruiz Jr. next. The list goes on – there's so many out there that I'd love to compete with."
Joshua's immediate focus is on avenging the shock defeat to Ruiz Jr. in New York in June, when his world title reign and unbeaten record abruptly ended.
"It's been a journey," he said.
"A lot of highs and a lot of lows, from the amateurs to the pros.
"Through the process you gain experience which has led me to this point in my life."
Part of Joshua's revamped training for his rematch with Ruiz Jr. will be to improve his agility, according to promoter Eddie Hearn.
"I think movement and looseness in this fight is quite important for him," Hearn told Sky Sports. "He's got to have that movement with him as well.
"I think with AJ, it's never about the weight, it's more about how he feels, how he's training, what he's doing.
"Against [original opponent for the fight against Ruiz Jr] Jarrell Miller, it was more about size, because he was going to get walked down. He wanted to be big, strong, solid. Obviously against Ruiz, someone that's faster, it's probably better to be a little bit lighter and more fluid.
"I think there will probably be a little bit of focus on being that way in this fight, rather than preparing for Jarrell Miller, like they did for 70 per cent of their camp last time."