The 24-year-old German international, who is sidelined with a back injury, will sign with the six-time Italian champions as early as this week, reports from Italy have suggested.
The midfielder can leave Liverpool on a free transfer at the end of the season, and 'Gazzetta' have reported that the German has already agreed a deal worth €6million ($7.5 million) per year.
French champions Paris Saint-Germain were also reported to be interested in signing Can who preferred a move to Italy with fellow Germans Sami Khedira and Benedikt Howedes already in Turin.
Can arrived in Liverpool in 2014 from Bayer Leverkusen, having previously won the Bundesliga title with Bayern Munich in 2013, and has made 166 appearances for the Merseyside club.