The newspaper reported that the two clubs have 'agreed on everything' and the move is set to take place at the end of the season.
The 28-year-old is expected to be the replacement of current Juventus right-back Stephan Lichsteiner whose contract runs out this summer.
Darmian has struggled for game time in Jose Mourinho's side this season, appearing on just four occasions in the league for the 'Red Devils' this season.
The Italian joined United for £13 million from Torino back in 2015 and now his return to the Italian city is all but confirmed. This time, however, he'll wear the famous black and white of Juventus.