The midfielder has enjoyed a successful 2012-13 campaign, and he says he wants to play for a manager who "really wants" him on his side.
The Belgian has enjoyed his most productive campaign at Goodison Park to date, scoring 12 goals in all competitions from the middle of the park.
Man Utd is reportedly keen to bolster its midfield, and speculation has quickly risen that Moyes, who will replace the retiring Sir Alex Ferguson after United's final game of the season at West Brom, will look to bring his Everton talisman with him to Old Trafford.
Speaking to reporters ahead of Everton's concluding clash of the campaign against Chelsea, Fellaini paid tribute to his current boss and refused to rule out a move away from Merseyside.
"If I’m leaving Everton - I say if - it will depend on lots of factors," said Fellaini, who reportedly has a 23 million pound buy-out clause written into his current contract. "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."
The former Standard Liege man attributes his goalscoring exploits this season to a change in position, which has seen him operating just behind the lone striker. Further fuelling the rumors of a possible move to the Red Devils, Fellaini revealed that both he and Moyes believe his best position is from a deeper midfield role.
"I’m happy with my season, although I didn’t play in my best position," Fellaini said. "I’m not a No. 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."