United boss Jose Mourinho is understood to have been interested in bringing the France international to Old Trafford last summer, only for Matuidi to choose Juventus above the Red Devils when leaving Paris Saint-Germain.
However, questions over the form and fitness of Paul Pogba this season have reportedly led Mourinho to consider bringing in further midfield reinforcements this summer, particularly as club captain Michael Carrick is set to retire at the end of the campaign.
Rai Sport reports that United have been in touch with Matuidi's agent Mino Raiola over a possible deal, although Juventus are unwilling to allow the 30-year-old to leave the club.
The player joined Juve for just €20m (£17.8m), but it would likely take a significantly higher bid to prise him away from the Italian champions, with his contract not expiring until 2020.
Matuidi has made 33 appearances in all competitions for Juventus this season.