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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.