Since the summer, Juventus have frequently been linked with a move for Can, who has just over six months remaining on his contract at Anfield.
The German international is able to hold discussions with foreign clubs at the start of 2018 but according to Tuttomercatoweb, Juventus have all but sealed a deal for the 23-year-old.
Earlier on Friday, Liverpool boss Jurgen Klopp had suggested that he remained hopeful of agreeing an improved contract with one of his key men, but it appears that Can has opted to take on a new challenge in the summer.
Juventus could potentially try to land Can in January, with Liverpool only able to recoup a fee if they choose to sell the player in the New Year.
Can has made 12 starts for Liverpool in all competitions this season.