That is the view of British compatriot Amir Khan, who said the heavyweight star needed to raise his profile in the US to become a "global star".
Khan has fought several times in the States, most recently against Saul 'Canelo' Alvarez in Las Vegas, where the Mexican scored a sixth-round knockout in May 2016.
But it was a big-money bout for Khan and brought with it the kind of attention that he feels Joshua – who faces Joseph Parker on March 31 in Cardiff – would easily attract if he showed off his skills for a stateside audience.
— Anthony Joshua (@anthonyfjoshua) February 5, 2018
"When you fight in America you become that global star, and that's what I did," Khan, who takes on Phil Lo Greco in Liverpool on April 21, said in quotes reported by Sky Sports.
"People around the world now, wherever I go, they will recognise me because of US television, how they promote you.
"One thing about the heavyweight division that AJ should definitely watch is – it's always been big in America with Muhammad Ali, George Foreman, Joe Frazier, Evander Holyfield.
"Why not fight in a country where heavyweight boxing is big?
"If he wants to make a big name, I think he might want to fight there first.
"He will build his name up, he will get a good knockout against some up and coming fighter, and then he will be ready, because people will see him live on TV and live in America.
"They will be like: 'This fight needs to happen now.'
"That's a fight people want to see in America, they are already talking about AJ. I think he should go there."
Joshua will put his IBF and WBA belts on the line next month against Parker, whose WBO strap will also go to the victor.