The 25-year-old has been heavily linked with a move away from Goodison Park this summer, and the reigning Premier League champions have been touted as the Belgium international's most likely destination.
New Red Devils boss David Moyes - who succeeded Sir Alex Ferguson at Old Trafford last month - has been credited with an interest in a number of his former Toffees players, and has already been knocked back in his attempt to sign sought-after left-back Leighton Baines.
Fellaini is also understood to be on Manchester United's radar, though, as Moyes looks to strengthen hissquad ahead of the 2013/14 campaign with the addition of the box-to-box midfielder.
Having had two bids for Barcelona's Cesc Fabregas already turned down this transfer window, Manchester United might now turn their attention to the Everton star.
However, the club will have to move quickly if they want to activate Fellaini's release-clause, which expires on July 31.