The 19-year-old striker was given an international call-up for the first time by Deschamps for the friendly games against Portugal and Serbia.
Martial, who joined Monaco in 2013 from Lyon, has slowly risen up the French international ranks having played at all youth levels.
A statement on the French Football Federation website read: "Anthony Martial requested permission from Didier Deschamps to travel to England to sign a contract with Manchester United.
"Given the exceptional circumstances, the coach has agreed to the request of the player."
Martial is due to return to the French training base at Clairefontaine, south of Paris, on Tuesday morning, the FFF added.
Reports have said that Manchester United could be willing to pay up to €50 million (£36 million, $56 million) for Martial who cost Monaco just €5 million when they bought him from Lyon.