Yet if he does not do so then United face the prospect of a player who turns 30 next week, and so is in his prime, walking away for nothing. It now seems as though Fellaini will move clubs in the near future, as United look to recoup money for the Belgian rather than let his contract run down.
Player contract regulations stipulate they can negotiate a transfer six months before their current agreement expires.
The sensational suggestion of Arsenal's interest will come as unwelcome news for Besiktas who had been tracking Fellaini for some time.
Felllaini was the first signing of David Moyes' ill-fated era as Manchester United boss, arriving on a £27m deal in August 2013.
Alex Livesey GettyImages
The much-maligned former Everton man has become a more frequent member of the United first team under Jose Mourinho, with the Portuguese manager having entrusted Fellaini with increased game time since taking the helm from Louis van Gaal in 2016.
Fellaini is out of contract next June, and is locked in contract negotiations with Old Trafford chiefs.
Jose Mourinho now sees Valencia's Carlos Soler as his main January transfer target, in what is likely to be a limited window for Manchester United.
Last month, Mourinho also admitted that he was "worried" about Fellaini's contract situation.
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