The experienced France international played for Roma for seven years before joining Milan on a free transfer in 2011.
The 31-year-old has only played 11 Serie A fixtures for the Rossoneri this season amid injury concerns.
Mexes’ current contract with the San Siro side expires in the summer of 2015.
United need at least one central defender this summer and could also look to replace ageing left-back Patrice Evra.
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