The French winger and his Old Trafford boss fell out during the summer, with Martial fined £180,000 for being AWOL after the birth of his son.
Mourinho has used Martial just once this season, hauling him off after an hour of the defeat at Brighton.
The player had been involved in discussions to extend his deal, as revealed by SunSport in May.
But the player is reluctant to commit while out of favour.
Martial is among a number of stars who are not featuring regularly, but could outstay Mourinho.
The Portuguese manager has come under increasing pressure after United’s spluttering start to the campaign — and has a history of leaving clubs during his third season in charge.
The Old Trafford hierarchy are keen to keep Martial, who joined three years ago from Monaco in a deal that could cost £57.6million.
He has this season left on his current deal, with the club holding an option for another year.
United will almost certainly trigger his extra year but his value will fall next season without a fresh contract agreed.
Paul Pogba has also thrown his future at United into doubt by claiming that the next few months will decide where his future lies.
Marouane Fellaini has returned to United from Belgium duty with a back problem – but he expects to be fit for next Saturday’s clash at Watford.
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