Reports earlier this week had claimed Milan had jumped to the front of the queue to sign the Portuguese star, and were prepared to sanction a £12m bid.
But the former-Sporting Lisbon star now looks to be the subject of a transfer tussle, with Juventus keen to snare the 25-year-old before their Italian title rivals get the chance.
Nani joined Manchester United in 2007 from the same Portuguese club as former-United star Cristiano Ronaldo, and has since gone on to make more than 200 appearances for the Old Trafford club.
But the Portuguese star has reportedly fallen out of favour at United, as contract talks continue to drag on with seemingly no resolution in sight.
Nani was left out of Sir Alex Ferguson's squad to face Newcastle, and looks to have dropped behind Antonio Valencia, Ashley Young, and Danny Welbeck at Old Trafford, and an now exit looks likely.
Juventus were heavily linked with the United star last month, but dropped out of the race as Milan took pole position to sign the Portugal international.
The Serie 'A' champions have now reportedly rejoined the race, although it remains to be seen whether they can match United's £20m valuation for the winger.
Juventus currently sit top of the table in Italy after six wins from their opening seven league games, as they look to defend their title.
Manchester United find themselves in second place in the Premier League, four points behind league leaders Chelsea.