The Sunday Mirror reports that United boss Sir Alex Ferguson is a big admirer of the Belgian international.
Reports claim Everton boss David Moyes would consider letting Fellaini leave in the January transfer window.
Fellaini recently stated that he would spend just another year at Goodison Park.
Moyes said: “I have got no problem if other clubs start circling for my players. None at all.
“What I do know is that they can’t come in and take any of my players until January and we are only in September.
“Whatever happens now, whatever Fellaini says, he is here for at least the next four months.
“He might be here even longer than that, I don’t know.
“What I do know for certain, though, is that Fellaini has got a five-year contract here.
“So clubs can circle, but the window has just shut, and we’re in a strong position as far as his contract is concerned.”
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?