Wilder will defend his WBC crown next month against Fury, with a third fight already agreed between the pair no matter the outcome of the rematch.
But Joshua has intentions of forcing an undisputed fight with the American, with talks underway to tempt his fellow world heavyweight champion to meet him instead.
“We’ve had meetings. That same meeting with Usyk’s manager, afterwards we had another meeting to potentially put an offer in to solidify [a fight with Wilder] before they have even had their fight, and before I have my next fight,” Joshua told Sky Sports.
“Everyone wants Wilder to win because [a fight with me] is what everyone wants to see. Wilder has a great right hand, I have a great left hand. It is a great boxing match.
“We had a meeting about that. It has great potential. I heard [Wilder and Fury] have a third fight lined up towards the end of the year but we have to throw a curveball in there.
“Something that gets Wilder’s attention providing he wins so that he thinks to himself: ‘Even though I have a rematch clause, I’ll see how I can manipulate my contract, get out of it, and fight for the undisputed championship’.”
Fury, meanwhile, intends to face Joshua and Dillian Whyte once the chapter of his career with Wilder finishes.
“I’ve got three more fights left,’ Fury told iFL TV. “Wilder next, Joshua then Dillian Whyte, then I’m out.
“Dillian has been mandatory for something like 2,000 days and hasn’t had a world title shot so when I beat Wilder I’ll give him a shot.
“He can be a defence, for sure. One of my last three. Wilder, Joshua, Whyte, done.”