France Under-21 international Martial was called up to the senior national team for the first time on 28 August.
“Anthony Martial asked France coach Didier Deschamps for permission to travel to England to sign a contract with Manchester United,” a statement from the French Football Federation confirmed.
Manchester United are set to complete the £36m signing of Monaco forward Anthony Martial.
The 19-year-old, who has been linked with Arsenal, was allowed to leave the France squad on Monday to travel for a medical with Louis van Gaal’s side.
Martial scored eight goals in 31 Ligue 1 appearances last season.
Should he sign, Martial will become Manchester United’s third most expensive signing, after £59.7m Angel Di Maria and £37.1m Juan Mata.
Spain midfielder Mata joined from Premier League rivals Chelsea in January 2014, while Argentina winger Di Maria moved from La Liga giants Real Madrid for a British record fee in August last year.
After Manchester United lost 2-1 to Swansea on Sunday, Van Gaal said he would not panic buy before the transfer window closes in England at 18:00 BST on Tuesday.