The former heavyweight world champion's return to the ring has been delayed by elbow surgery but he is still keen to make a fight with Fury, who has been dropping hints about coming out of retirement.
Joshua told BoxNation: "Hopefully [the Fury fight] happens.
"The industry should not be left without it, and those [who are] interested should be able to witness it."
The fighter has a number of other opponents in mind if a long-awaited bout with Fury doesn't come to fruition.
Joshua said: "I think a potential fight with Martin Bakole, Agit Kabayel or Deontay Wilder would work too.
"To be completely honest with you, Joseph Parker deserves a shot at the winner [of Usyk vs Dubois 2] more than me right now."
Joshua hasn't fought since his bruising defeat to Daniel Dubois last September and is determined to ensure that his body is in the right condition so he can attempt to become world champion for a third time.
He said: "My body has been through the works.
"If I want to be here for the long time I just want to make sure my body is really really good before I get back into the ring.
"Sooner than later. I'm still training but I'm just kind of rebuilding.
"To be good is not enough in boxing, if you want to be a world champion you've got to be great.
"Throughout the last year or so, especially my last fight, I was good but not great.
"To be a champion you gotta be 'on your s***' basically and I need to step my game up."