According to English publication, The Times, Martial is considering signing a new long-term contract at United because he believes he can outlast Mourinho at the club.
The much-maligned Mourinho is understood to have suffered disagreements over the future of the 22-year-old with vice-executive chairman Ed Woodward.
The Red Devils have offered a new five-year deal to Martial and are hopeful that the Frenchman will sign it even though the former Chelsea boss deemed him surplus to requirements.
It's been claimed Woodward believes MOus has yet got the best out of the former AS Monaco man and refused to sanction his sale for Mourinho to bring in Willian or Ivan Perisic, who are 30 and 29 respectively.
Despite the public backing of the board, Mourinho's position will come under review if United lose away to Burnley on Sunday to make it three losses in a row.