Nani put pen to paper on a new long-term contract last year, but has struggled for game time this season and could be sold in the summer.
The Manchester United man has made just seven starts this season, and reports last week suggested that Juventus were once more interested in ending his seven-year stay at Old Trafford once more having been linked with him last year.
According to Tuttosport, Juventus are now on the verge of completing the deal, and have also moved for Barcelona winger Alexis Sanchez.
The Chilean signed for the Catalan club from Udinese in 2011, but could be on his way back to Italy.
The paper adds that the pair will spearhead Juventus' tactical switch to 4-3-3 next season as they look to make an impact in Europe.
The Turin-based outfit have won the Serie A title for the past three seasons, but were knocked out of the Champions League at the group stages, and failed to make the Europa League final, which will be hosted at the Juventus Stadium, having been eliminated by Benfica.
Nani could be just one of a host of departures from Manchester United this summer. Nemanja Vidic is on his way to Inter Milan, while Rio Ferdinand and Patrice Evra could also follow him out of the Old Trafford exit.
It is likely to be a frantic summer for Barcelona too, with a new manager expected to take over at the Nou Camp and problems in goal and in defence needing to be addressed.