The arrival of Alexis Sanchez from Arsenal has seen the Frenchman shifted from the left of his side's attack to the right, a position he struggled to perform in during Sunday's 1-0 defeat against Newcastle.
Before the loss at St James' Park, Martial was dropped from the team that beat Huddersfield, replaced by youngster Scott McTominay.
Mourinho is reportedly looking to reassure the 22-year-old that he has an important part to play at the club.
Martial, though, is believed to be assessing his options having grown increasingly frustrated in recent weeks.
Both Paris Saint-Germain and Arsenal are said to be interested in the former Monaco man, with the latter having made a bid for him as a possible makeweight in the Sanchez deal.
That offer was rejected straight away, however, an indication of United's desire to keep Martial at the club for the long-term.
An Old Trafford source, according to the Sun, 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.
“PSG and Arsenal both want him but Jose still has plenty of faith in his talents and rates him highly.
“Jose feels he has a huge role to play in this season and the coming ones. He’s a big fan of the lad.”