Former undisputed middleweight champion Hopkins believes that the Englishman is capable of more but must prove himself against the United States' best fighters.
"What [Joshua] needs to do is to come to America and fight the top champions, if they are willing to fight. The top contenders, if they are willing to fight," Hopkins told reporters.
"He has the ingredients, he definitely has the personality and he can flat out fight. A superstar in the making. He is in the position to become the face of the heavyweight division. Right now, I can't give him that."
A potential bout against Wilder, who is undefeated since turning professional in 2008, has been reported, should Joshua defeat Pulev next month.
Hopkins continued: "I think [Joshua] is more savvy, the veteran – even though he is not a veteran.
"He has experience and he'll fight with great confidence. I have to give the edge to him, I really do. Not a big edge, but I have to give it to Joshua based on not just his size – but that's a factor – but the way he believes in himself. Look how he fights."
Joshua's bout against Pulev in October is expected to be watched by almost 80,000 inside Cardiff's Principality Stadium.