The Belgian international has long been linked with a move away from Goodison Park, and after a deal in January failed to materialise, he again looks set for a summer of speculation about his future.
Chelsea and Arsenal had been linked, but now he has one eye on Old Trafford due to the fact Moyes is taking charge.
"If I'm leaving Everton, I say if, it will depend on lots of factors," Fellaini told the Sunday Mirror.
"I only want to go to a club where the manager really wants me. In 2008, Everton did everything to convince me, especially David Moyes. He made me the player I am now."
Fellaini also revealed that Moyes had told him that he wanted him to become a deep-lying midfielder - rather than the forward he had emerged as in recent years.
"I'm happy with my season, although I didn't play in my best position," said Fellaini.
"I'm not a number 10. David Moyes predicts my future as a defensive midfielder, but due to a lack of offensive power, he plays me up front.
"In the future I want to play as a six or an eight. From there, I can create danger and score goals."