Can, 23, has entered the final year of his contract on Merseyside and despite talks over a new deal there is still no sign of a breakthrough being reached.
Juventus initially made a move for the Bayern Munich academy graduate towards the end of the summer transfer window, reportedly tabling an offer of £22.6m. The club are instead now looking to bring the midfielder to the club on a free transfer at the end of the season and are free to come to a pre-contract agreement with the player as of 1 January.
Juve chief executive Beppe Marotta has already confirmed the club are hoping to sign Can, along with another Germany international approaching the end of his current deal in Schalke midfielder Leon Goretzka.
Despite speculation over his future, he remains a regular in the Liverpool side, starting nine of his side's 13 league matches this term including the 3-0 win over Stoke City.
Speaking to Spox after that win, Can suggested talks with Liverpool over a new deal are still alive, adding his focus remains on their fortunes this season.
"I clearly talk to Liverpool, let's see what happens. I focus only on Liverpool and the rest my adviser takes care of."
Liverpool boss Jurgen Klopp has also not given up hope of his countryman penning a fresh deal on Merseyside. He told a press conference last Friday: "[Can] could still sign a contract in May. We want to keep him. We have to be as attractive as possible as a club."
Should Can become set on leaving Merseyside, his club may be tempted to try and cash in on him during the January transfer window. But reports suggest Liverpool are not and are determined to hold onto the player until the end of the season believing a new deal is still a possibility.