Can has long been expected to move to Turin this summer, when his deal at Anfield will expire. Liverpool have been unable to agree fresh terms with the 24-year-old, and are resigned to his departure.
An announcement is likely to be made once Liverpool have played their Champions League final with Real Madrid on May 26.
Can was this week left out of the Germany squad for this summer's World Cup in Russia having missed the last two months of the season with a back problem.
He travelled with Jurgen Klopp's squad for their warm-weather training camp in Marbella on Wednesday, and is set to resume training in Spain. That raises the possibility of the former Bayern Munich man being involved against Real Madrid a week on Saturday, though he would need to prove his fitness to Klopp before he could even be considered for a place on the bench.
Can joined Liverpool from Bayer Leverkusen in 2014 and has made 166 appearances since, scoring 14 goals.
He has been the subject of interest from numerous clubs once it became apparent that a new deal at Anfield was unlikely. Manchester City, former club Bayern Munich and Borussia Dortmund have all made enquiries, but Juventus appear to have won the race as the Bianconeri look to re-shape their team next season.
Liverpool, meanwhile, will complete the signing of Naby Keita from RB Leipzig on July 1 , with the Reds set to pay a total of £52.75m for the Guinea star. Klopp is expected to target at least one more midfielder this summer, with his need heightened by Can's imminent exit.
Meanwhile, young forward Yan Dhanda is set to join Swansea upon the expiry of his Reds contract next month.