Can is out of contract this summer and he will leave the Reds on a free transfer.
The report adds that the Liverpool midfielder will earn around €6m/year over the next five years at Juventus (after tax).
The 24-year-old has been a key player for Jurgen Klopp and losing him for nothing is a massive blow. It will be interesting to see how Liverpool cope with this departure.
The Reds are yet to sign a replacement for Philippe Coutinho. The Brazilian left the club in January.
Naby Keita is set to come in at the end of this season but the Leipzig star is not similar to Can in terms of skill set and style.
Liverpool have been linked with the likes of Jorginho and Ruben Neves this month and they would be the perfect alternative to the German.