Martial expressed a willingness to leave Old Trafford recently over a lack of game time following the arrivals of Jadon Sancho and Cristiano Ronaldo at the start of the season.
The Spanish club do not have the option to buy Martial permanently at the end of his loan spell.
Martial was signed for the Red Devils by Louis Van Gaal on the last day of the summer transfer window in 2015 as the most expensive teenager in world football.
The then 19-year-old was brought in from AS Monaco for £36m and he announced his presence with a wonderful solo effort against Liverpool on his debut.
Martial has gone on to score 79 goals in 269 games for the Red Devils, winning one FA Cup, one League Cup and the Europa League but he has fallen down the pecking order following the arrivals of Edinson Cavani, Ronaldo and Sancho.
The 26-year-old started just two Premier League games this season, and made 11 appearances in all competitions.
United interim manager Ralph Rangnick recently accused Martial of refusing to avail himself for a Premier League game at Aston Villa; an assertion the Frenchman denied.
Sevilla are currently second on the La Liga table, four points behind leaders Real Madrid.
