The Sun says he is planning to sit down with Martial to give him assurances over his United future.
The ex-Monaco ace was played out-of-position in United's 1-0 away loss to Newcastle yesterday.
But Mourinho is now keen to ease the 22-year-old's fears and affirm he is still in his future plans.
Martial is understood to be assessing his options and will wait and see how the season pans out.
An Old Trafford source said: “The boss is ready to sit down with Anthony to put his mind at rest.
“His position is under threat and there are worries from him. He is going to wait and see what happens.
“Jose feels he has a huge role to play in this season and the coming ones. He's a big fan of the lad."