According to RMC Sport, Martial has rejected a five-year contract extension offered by United.
The 22-year-old is under contract at Old Trafford until 2019. He has the option to add an extra, but would rather not trigger that clause.
The France international no longer feels important at the club and relations with boss Mourinho have turned frosty.
Juventus, Spurs and Atletico Madrid are all interested in acquiring the his services, if United decide to sell him.