The Serie A champions snapped up Paul Pogba from United last summer on a free transfer, and are believed to be keen to bring Anderson into their midfield next.
The Brazil international has struggled to cement a place in the United first-team since his big-money move from Porto in 2007.
He's failed to progress from talented teenager to world class midfielder, and with the arrival of Marouane Fellaini, he could find opportunities limited.
The report claims Juve pondered a move for the 25-year-old in the summer transfer window, but David Moyes was reluctant to lose any of his first-team players in his first few months at the club.
Next summer though, the Brazil international could be back on the chopping block and Juventus are reportedly willing to wait until then to make a bid.
But central midfield is not an area of real strength for United compared to the rest of their squad, despite the £27.5m addition of Fellaini.
The club were linked with a whole host of midfielders, including Ander Herrera, Cesc Fabregas and Sami Khedira with only Tom Cleverley and Anderson available as back-ups to Michael Carrick.
Juventus on the other hand are strong in the position, with former-United star Paul Pogba last season's break-out star.
Andrea Pirlo, Arturo Vidal and Claudio Marchisio - all established internationals - also occupy central berths for the Italian giants.