French newspaper Le 10 Sport claims that Evra is considering taking on a new challenge at the end of the season, and could be tempted by a move back to his native France.
The United defender has been at Old Trafford since he signed from Monaco in 2006, and the 32-year-old may return to his old club. Paris St Germain have also been linked.
The France international reportedly began to consider his future at United following Sir Alex Ferguson's announcement that he planned to retire at the conclusion of last season.
New boss David Moyes was keen to bring in another left-back over the summer - United failed in a deadline day move to bring Fabio Coentrao on loan from Real Madrid.
The report claims Evra has not made a final decision over his future yet, and will see how this season pans out and whether Moyes moves again to sign a left-back in the January window.
The defending Premier League champions have not got off to the best start, but the title race appears wide open this season.