According to Italian newspaper Il Tempo, the club have put a £130,000-a-week deal on the table for him to swap Rome for Old Trafford.
United are investing heavily this summer on their playing squad as Jose Mourinho attempts to bridge the gap to the top four in the Premier League. The extra demands of Champions League football will also need more strength in depth is needed.
Midfield is a key area Mourinho is hoping to add quality to, with the club already closing in on signing Chelsea star Nemanja Matic.