The future of the France international was the subject of much debate during the summer transfer window, with Martial keen to leave Old Trafford in search of more regular first-team football.
The Daily Star now claims that Mourinho is desperate to sell the attacker before the end of the European window, which closes on August 31, in order to raise money for January signings.
However, Woodward believes that the 22-year-old still has unfulfilled potential and is unwilling to sell him for anything other than top price.
Tensions are already thought to be running high between the pair following an underwhelming transfer window which saw United fail to land Mourinho's top target of a new central defender.
Interested clubs such as Bayern Munich are unwilling to meet Woodward's asking price for Martial, who has struggled for game time since the arrival of Alexis Sanchez in January.