The Belgian midfielder’s current deal is due up at the end of the season and there are intense rumours that he is eyeing a move to Turkish outfit Besiktas.
United boss Jose Mourinho has apparently offered the 29-year-old an extension but negotiations appear to have stalled.
The Red Devils supporters have struggled to take to Fellaini’s defensive style of play, but he has regularly been defended by boss Mourinho.
And now he is being strongly advised to stay on at Old Trafford by Sherwood.
“I suggest he gets the pen out and starts to sign the contract,” Sherwood told Sky Sports show ‘The Debate.’
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“The manager loves him. The way he has been speaking over the last couple of months he has been lauding him.
“It is perhaps a little bit over the top and perhaps a little bit false at times.
“But he affects the football match when he plays and when he comes off the bench he affects it.
“So why would you not want to stay at Manchester United for the rest of your career.
“At Manchester United the most important person you want to like you is the manager.
“I think that Jose thinks that he likes Fellaini. Unless he has got a better option out there, but I can’t see there being a better option out there than Manchester United.”