The 24-year-old spent has spent the first half of this season with Aston Villa - playing nine games in the Premier League - but will now continue his development elsewhere after agreeing a move to Serie A until the end of the season.
Manchester Evening News understands that United have executed the switch through intermediaries they have previously used to transfer players to Italian clubs.
Alexis Sanchez and Romelu Lukaku are among those to have headed there from Old Trafford in recent years.
Tuanzebe progressed through the famed United academy and has made 37 senior appearances for the club.