The 23-year old Belgium international has come along in leaps and bounds in recent times says Moyes who is confident the former Standard Liege man can be a star within three or four years.
"I've said all along I think Fellaini is a really good player in the Premier League," Moyes told the club's official website.
"And he's young. He's only 23 now so you think what he could be like when he's 26 or 27.
"But we think he's already come on a lot. He's physically stronger, much more disciplined in the job he has to do in the team.
"He still has a tendency to run out of position but that can upset the opposition because of his size and you saw how good his feet are.
"I think he's a real good player. He's got a lot going for him."