Can, 23, has entered the final year of his contract at Anfield and while talks over a new deal have been ongoing 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 before turning their attention to France international Blaise Matuidi.
While that bid failed, there interest has remained. The Bianconeri and other clubs from outside England are able to hold talks with the midfielder in January to try and convince him to sign a pre-contract agreement. Juventus are now stepping up their attempts to sway Can and his representatives, according to Tuttosport, who add that the Liverpool midfielder and his people "are not hiding and have no reason to do so" given they will be free to speak to other clubs next year.
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 the report suggest Liverpool are not minded to make a deal and are determined to hold onto the player until the end of the season.
Can has so far remained coy on his future, insisting he is currently focused on Liverpool's current campaign but was left unable to hide the fact he is flattered by interest from the Serie A champions.
"It's always an honour to receive an offer from such a renowned club, but currently I am only focused on the season with Liverpool," Can told German newspaper Kicker in October.
"My agent takes care of the rest. The Premier League is just a really cool league, the most interesting in the world, but you must respect other big clubs and leagues.
"You never know what will happen. And I don't know what Jurgen Klopp plans."