The former five-division champion says Joshua has to choose how he wants to be remembered by world boxing fans.
Sugar Ray was present in the UK to witness Joshua impressive knock down of Alexandra Povetkin in the seventh round.
The 67-year-old boxing legend believes the Brit must fight in the US to validate his status as a world star.
The American speaking to SunSport said:
“It all boils down to what Anthony Joshua wants and what he believes in.
“You have to ask him the question: what do you want to be? How do you want people to remember you?
“Do you want to just be remembered here or global? I’m sure it’s global.
“In America they know the name Anthony Joshua but they have not all seen him.
“There are a lot of boxing fans, millions of boxing fans, but they have not all seen what he is about yet.”
Joshua’s next fight is scheduled for April 13th at Wembley where he regularly has a full capacity.
Leonard who competed between 1977-1997 acknowledges Joshua is doing right with the kind of crowd he pulls but still wants him to come to America.
“He is going down the right road,” the 62-year-old continued.
“America will be the next key.
“I was in Cardiff for the [Joseph] Parker fight so I’d had a taste of the Joshua mayhem over here before Wembley.
“They absolutely love him, they support him and I truly believe he feeds off that. He is getting better and better.
“He is doing what he is doing over here but to recreate it in America… that is the key. That is indeed the key and the purpose.”