The Premier League champions are expected to make major changes to their playing staff this summer after a poor season domestically this term under David Moyes.
One of the priorities is in the centre of the park, where the likes of Marouane Fellaini and Tom Cleverley have come under increasing criticism this season.
The Italian press claim that United have turned their attention to Montolivo and feel the experienced midfielder can add to the dynamic of their team.
The Italy international has played 22 times for the San Siro side this season, scoring twice.
With Milan having a similarly underwhelming campaign, things are also set to be shaken up at the Italian club, with new faces and sales expected.
As such Clarence Seedorf’s men may well feel that it could be time to cash in on Montolivo.
The 29-year-old is widely expected to add to his 57 national caps for the Azzurri this summer in the World Cup.