Martial's stock at Old Trafford fell somewhat last term following a blistering first season under Louis van Gaal in which he finished as the club's top scorer. Under Jose Mourinho, the France international has struggled to recapture the form that saw him named the 2015 Golden Boy, the award handed down to the best young player in Europe under the age of 21.
He was left on the sidelines for long spells in 2016-17, managing just four league goals in 24 games and making only 18 top-flight starts.
The 21-year-old has since been linked with a move to north London, with the Daily Mail reporting that Arsene Wenger is prepared to sanction a £40m ($51m) bid for the forward should the club fail to sign Kylian Mbappe this summer.
Fresh reports have also claimed Martial will seek talks with Mourinho with the intention of leaving the club this summer. The United forward has come out to rubbish those claims, however, tweeting to his 918,000 followers: "The rumours are false."
RMC Sport also report claims of a meeting between Mourinho and Martial or his representatives are untrue.
Martial's agent, Philippe Lamboley, did sit down with United executive vice-chairman Ed Woodward following the end of the 2016-17 season, but a move away from Old Trafford was not discussed.
"I wish all 21-year-old players had already played as much of professional matches as Martial. Anthony's career is simply outstanding. He has two years left and there is no reason for him to leave Manchester United," Lamboley told Journal du Dimanche.
"If Ed Woodward calls me to tell me he wants to see him leave, then things will be different. But that is not what he told me during our last meeting."