The former Nice and AS Monaco player joined the Red Devils in January 2006, and has been in good form this season.
His current deal runs out next summer, and with United struggling to find a natural replacement, they look set to keep the 31-year-old.
Evra has had a prolific campaign, scoring four times – the most he has achieved in any of his seven previous seasons at Old Trafford.
PSG have shown interest in Evra, and did consider making a £5m bid in January, before electing to look at alternative targets.
Sir Alex Ferguson has struggled to find adequate cover at left back for Evra. He signed Alexander Buttner from Vitesse Arnhem in the summer, but he has largely unimpressed when he has been given the chance to play.
United owned defender Fabio, who is currently on loan at QPR, has had an injury-hit campaign at Loftus Road.
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