Evra's contract at Old Trafford expires this summer and no new deal has been agreed as yet.
United have been linked with a number of left-backs, including Southampton's Luke Shaw as they weigh up possible replacements for Evra.
A host of clubs, including Evra's former side Monaco, have been linked with a move for the full-back, but it appears Inter Milan are in pole position to land the 32-year-old.
Inter are keen to reshape their squad after a disappointing campaign in Serie A and they see Evra's experience as a key addition to their squad for next season.
Should Evra make the move to the San Siro, he will be reunited with Nemanja Vidic at Inter after the Serbian defender agreed a deal to join the Italian giants this summer when his contract at United expires.
Evra moved to Old Trafford from Monaco in 2006 and established himself as first-choice left-back for United upon his arrival.