The 33-year-old made 45 appearances for United in all competitions this year in a disappointing season, which had the Old Trafford outfit finish seventh.
Evra, who join United from Monaco for £5.5m in 2006, has won five Premier League titles, three League Cups and the Champions League.
His decision to remain at the 20-time league title winners is understood not to have any impact on the club's pursuit of Southampton defender Luke Shaw.
United have already lost three of their senior players ahead of the opening summer transfer window, with Nemanja Vidic on his way to Inter Milan, Ryan Giggs having put an end to his 23 years of glittering playing career and defender Rio Ferdinand announcing he will leave the club.
Giggs will serve as assistant coach to the new United boss Louis van Gaal in the coming seasons.
