Evra will be out of contract come the end of the season and could join teammate Nemanja Vidic at the Serie A club.
So far the floundering Premier League champions have showed no inclination to offer him a new one. Even then, it is only like to be a one-year extension.
That has opened the door for Inter to lure the Frenchman to Milan with the kind of lucrative, longer-term deal that has persuaded Vidic to swap Old Trafford for the San Siro.
The United skipper will strengthen Inter in central defence but the club are also in the market for a full-back.
The Mail also quotes Evra speaking about his passion for United and what he will do if he must leave Old Trafford.
"My love will not change for the club," he said. "I love Manchester. When my love will be broken with Manchester, I will study the possibilities."
Despite thoughts of Evra's departure, the Frenchman has still very much been David Moyes' first-choice left-back. He has appeared 32 times for the Red Devils this year, per WhoScored.
Moyes has kept faith with Evra despite the club's poor performances. This trust has been reciprocated by Evra, as sports writer Kevin Palmer tweeted:
Evra has been a magnificent servant for United, but it is time for him to be moved on. He is one of the leaders of the squad, but as performances have shown, the fallen Manchester giants need a fresh angle when it comes to who inspires the team.
Evra's attacking instincts remain intact, but he is a huge liability from a defensive standpoint. He has lost the pace that made him one of the best in the world in his position.
This is reflected in the fact that United have conceded more than a goal a game during 2013/14, with 31 goals being lost, per Squawka. This is both unacceptable and unexpected for a club like United, and Evra is a huge part of the blood and the bones of the team's defensive body.
His influence on results has definitely not been wholly positive for some time. His direct mistakes against Tottenham Hotspur and Cardiff City have cost Moyes vital points. This could well end up as the difference between Champions League football and no European competition at all for the Red Devils in 2014-15.
Will United sign Luke Shaw as Patrice Evra's replacement?
United need to look elsewhere for a left-back after the failed attempt to land Leighton Baines in the last two transfer windows, per BBC Sport. As the club are to lose Vidic as well, it might be a case that Moyes looks toward bringing in an experienced defender to replace Evra.
The legend behind Southampton's Luke Shaw is growing by the month, but it is questionable if United will spend a huge fee on one so young.
Shaw has shown similar qualities to Gareth Bale at the same age, and as United aim to find their next big star in the summer, Shaw is shining brighter than most right now.
Much will depend on how far Moyes looks into the future. His job security is lessening with every big loss, so a ready-made replacement for Evra—rather than a prospect like Shaw—might be favoured.