The Serbia international has been linked with a move to Old Trafford for some time after an impressive spell in Florence.
Gianluca Di Marzio reports that United made an approach to the Serie A club about the 21-year-old two days ago.
The move marks the resumption of their interest in the defender, who can operate at centre-back or right-back.
Fiorentina received a €40 million bid from the Red Devils for Milenkovic in January, but turned it down as it failed to meet their valuation of €50m.
The Serbian featured regularly for La Viola last season, scoring three goals in 34 Serie A appearances.
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