However, the offer has come from Dominic Breazeale, who must beat Deontay Wilder this weekend to make the belt his own.
Joshua has been trying to fight WBC champion Wilder for well over a year but talks broke down because of financial differences.
If Breazeale pulls off a huge upset and emerges victorious this Saturday he has promised to offer Joshua a unification bout.
“Definitely. I would love to be back in the ring 90 days from Saturday night, me and Anthony Joshua, somewhere here on US soil,” Breazeale said.
Breazeale has fought Joshua once before – losing via a six-round knockout in 2016.
And he wants a rematch to try and become the unified world champion.
“I know Joshua’s making his debut June 1 here in New York.
“That would be one hell of a fight, a rematch between me and Joshua for the undisputed heavyweight championship in Las Vegas, Nevada.
“I think that would be something the world definitely needs to see.
“I’ve been fortunate enough to be in the ring with Andy Ruiz, he’s got fast hands, big punching power.
“He’s definitely got a hell of a shot.
“Do I think he’s got enough time to train for Anthony Joshua? Not quite sure.
“But if it goes the way I’m thinking it does, Andy Ruiz gets an early round stoppage because he’s going to come out guns blazing, that what he does. He’s a bad, bad man.
“But at the same, Joshua is a high calibre fighter, he’s fought some of the best in the world and he continues to do so.
“He could have took some nobody that crawled out of bed yesterday but instead he takes a high calibre guy like Andy Ruiz and he’s going to make a fight of it.
“He wants to make one hell of a debut here in the US and I’m looking forward to it. I’m glad to be part of the heavyweight division right now.”