Martial was set to be offered a lucrative new deal, however his relationship with Mourinho has soured to such an extent that he is reluctant to commit to a new deal.
The France forward was desperate to leave the club in the summer, but Woodward blocked any move.
Contract talks had been opened in May between Martial and the club, but he has now stepped back from negotiations, according to the Sun UK.
Mourinho has only used Martial once this season and hauled him off during a 3-2 defeat to Brighton. The player is now waiting to see what happens with the manager’s future at the club, before committing his own.
Martial only has one year left on his contract and while United have an option for a further year, they are determined not to reach next summer without him signing a new deal.