The Lazio midfielder was linked with a move to Old Trafford last summer, as Pogba looked to force through a move to Real Madrid.
But United were forced to pull out of a move for Savic, with Pogba’s move away falling through.
The 25-year-old has four goals and four assists in 24 Serie A starts this season, helping Lazio climb to second in the table where they sit just one point behind Juventus.
His displays this season have convinced United to step up their interest and bring him to Old Trafford in the summer, according to Il Messaggero.
Any move will depend on Pogba’s future, particularly with Lazio set to demand £107million for the Serbia international to leave the club.
United may face competition from Chelsea to sign him, with the midfielder reportedly one of Chelsea’s top targets in January.