The France forward has become a fringe figure at Old Trafford, making just two Premier League starts this season and only four in all competitions.
“We spoke at length on Wednesday,” said interim United manager Ralf Rangnick, revealing the 26-year-old’s desire to quit Old Trafford.
“He explained to me he’s been at Manchester United now for the last seven years and he feels it’s the right time for a change, to go somewhere else.
“I think in a way this is understandable, I could follow his thoughts but on the other hand, it’s also important to see the situation of the club.
“We have Covid times, we have three competitions in which we still have high ambitions and want to be as successful as we can be.”
Martial became the world’s most expensive teenage footballer when United signed him from Monaco in September 2015.
The £36million fee, potentially rising to £58m, made him United’s third most expensive signing at the time after Angel Di Maria and Juan Mata.
Martial made a memorable debut, coming off the bench to score a superb solo goal against Liverpool, and has gone on to score 79 goals in 268 appearances.
But he has fallen down the pecking order of United forwards following the arrival of Cristiano Ronaldo, Edinson Cavani and Jadon Sancho and the emergence of Mason Greenwood.
Rangnick confirmed there has been no interest in Martial ahead of the January transfer window and he could stay at United.
He said: “I told him listen, as long as there is no club showing interest in him, and it should not only be in the interest of the player it should also be in the interest of the club.
“So far, as far as I know, there has been no offer from any other club and as long as this is the case he will stay.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies