The 19-year-old has been given permission to leave the France squad to travel to England to sign a contract with the Premier League giants.
An official statement released by the French FA said: “Anthony Martial was presented Monday at 11:00 at the gathering of the France team at Clairefontaine . He requested from Didier Deschamps permission to travel to England to sign a contract with Manchester United.
“Given the exceptional circumstances, the coach has acceded to the request of the player.
“Anthony Martial left Clairefontaine Monday at 12:00. He will return on Tuesday morning.”
Martial has previously been linked with Chelsea and Tottenham.