The Daily Express reports that the Italian side are keen to force through a deal to sign the 27-year-old.
Nani only recently signed a new five-year contract with United and has featured more regularly for the club this season.
Monaco are also reportedly interested in the highly-rated winger.
Tuttosport reports that Juventus boss Antonio Conte is a fan of Nani and is keen to bring in the winger in January.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?