The 25-year-old missed the club's 2-1 win over Sunderland on Saturday and underwent scans on the injury, with United adamant the summer signing would not need immediate surgery.
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"In accordance with the [Manchester United] club doctor, Marouane Fellaini will have surgery in December-January, unless he is ruled out from playing beforehand anyway due to a suspension," said Van Crombrugge.
"After surgery we believe he will only need one or a maximum of two weeks to recover. After that he can resume playing by using a brace. The surgery is not urgent, hence the delay.
"Last weekend he could not play for Manchester United because he had too much pain but because he is now taped he can play."
Fellaini has made five appearances for the Red Devils since leaving Everton on transfer deadline day, though has yet to open his account for the reigning Premier League champions.