But the 21-year-old took to social media to dismiss the speculation, tweeting: "The rumours are false." His post was accompanied by a red dot to symbolise United.
Martial enjoyed a brilliant debut season at Old Trafford, in 2015/16, as he scored 11 Premier League goals and added four assists in 31 appearances following his move from Monaco, which made the world's most expensive teenager.
But his form dipped in his second campaign, under Jose Mourinho, as he was limited to just four goals in 25 Premier League appearances, though his assist total did jump to six.
Mourinho admitted late in the season Martial was not performing up to his expectations and he did not start Manchester United's Europa League final victory over Ajax.
Martial will face increased competition for a starting role next season with Mourinho aiming to add an attacking midfielder to his squad.
United have been in talks to sign Croatian international Ivan Perisic from Inter Milan. If he comes to Old Trafford he would likely compete with Martial to start on the left of midfield.
United CEO Ed Woodward has also been in negotiations to sign Spanish international striker Alvaro Morata from Real Madrid.
