The Frenchman, who has spent the last eight years with the Red Devils, has less than 12 months remaining on his current Man United contract.
Martial's deal contains an clause to extend by a further year, but Man United boss Erik ten Hag is currently unsure whether to take up the option.
According to The Sun, Man United's decision will depend on Martial's performance levels between now and the end of the season.
With Man United yet to make a firm decision over the player's future, Martial has effectively been challenged to show his worth to the club.
If they opt against extending his contract, Martial would be allowed to depart on a free transfer when his current deal expires in June 2024.
There is also the possibility that Man United could entertain offers in the January transfer window rather than let him leave for nothing next summer.
Martial was linked with a move away during the summer transfer window, amid interest from fellow Premier League club West Ham United and Turkish giants Fenerbahce.
There was also said to be links with the Saudi Pro League, but Martial was reluctant to complete a move to Saudi Arabia.
A recent report claimed that Man United have already received three offers for Martial ahead of the January transfer window.
While speculation continues to surround his future, Martial will look to prove himself on the pitch in the coming months.
Although the 27-year-old has made nine competitive appearances this season, he is currently behind summer signing Rasmus Hojlund in the pecking order.
Martial has scored just one goal this term, with his sole strike taking place in September's EFL Cup win over Crystal Palace.
The forward is expected to be in the squad for Saturday's Premier League away meeting with newly-promoted Sheffield United.