The pair have failed to agree a deal for the bout which was first spoken about in October 2017.
But Anthony Joshua’s manager Freddie Cunningham believes the solution could be to fight in both Britain and the US.
Speaking to Sky Sports, Cunningham said: “I think if the fight is going to happen, it’s going to be a two-fight deal whatever, so it’s going to be one here and one there.
“It makes sense to do it that way. They are both huge names in their territories.
“Why not give the fans in America what they want and give the British fans what they want? So, I think it will happen, possibly both, but I don’t know which way around.”
Since the fight was first discussed, Joshua has defeated Carlos Takam, Joseph Parker, and Alexander Povetkin, while Deontay Wilder has beaten Luis Ortiz, Dominic Breazeale, and drawn with Tyson Fury.
Joshua takes on Andy Ruiz Jr. at Madison Square Garden in New York on June 1 in what will be the Brits US debut.
It is important he puts on a dominant display after Wilder knocked out Breazeale in the first round to retain his WBC world title last weekend in an incredibly impressive display.
Meanwhile, fellow British heavyweight Fury will also fight in the US when he takes on Tom Schwarz on June 15.
Joshua’s decision to fight in the US comes after Wilder and Fury attracted a great deal of attention there last year when they fought to a thrilling, albeit controversial, draw.
On Joshua’s US appeal, Cunningham added: “It starts with the fighting, his style, what he brings to the ring, the knockout will be the first part.
“Outside of it, I think it’s just being himself. If you’re one of those guys that maybe talks the talk you only go so far.
“You need to be a bit wider and he’s got all the ingredients, he’s personable. I think the American public like him as well.
“They seem to get on well with him, it’s just showcasing who he is. Do everything in the ring, everything exciting there, and he can showcase who he is.”
Joshua will headline the Sky Sports Box Office card on June 1 with his fight scheduled for the early hours of Sunday morning UK time.
Katie Taylor, Callum Smith, Josh Kelly, Joshua Buatsi, and Tommy Coyle will all feature on the undercard.