News of the Italian giants' interest in Garay comes just a day after it was revealed Mats Hummels was happy at current side Borussia Dortmund.
Manchester United have been keeping close tabs on Garay during the past few seasons - but have never made an official bid for the centre-back.
However that could change this summer as Manchester United's new manager Louis van Gaal is looking to sign at least one experienced centre-back during the summer transfer window after losing both Ferdinand and Vidic.
Juventus' apparent desire to land former Real Madrid defender Garay could see Manchester United up the ante in their bid to sign the 27-year-old.
Van Gaal has reportedly handed Manchester United chief executive Ed Woodward a lengthy transfer shortlist - with Garay said to be one of the players the Dutchman has identified to replace the aforementioned Vidic and Ferdinand.