The Italian Serie A champions have been linked with a swoop for the 23-year-old, who has a contract at Anfield until next summer, throughout this pre-season.
Can has so far failed to sign an extension with the Reds and the club have reportedly placed a 30 million euro price-tag on his head.
Juve, who have also been linked with moves for the likes of Paris Saint-Germain star Blaise Matuidi and Sevilla's Steven N'Zonzi, seem to have now identified Can as their top target.
The Bianconeri coach Max Allegri is believed to be a big fan of the player and now he is inside the final year of his contract, they clearly feel the Reds will sell to avoid losing a vast amount of money on him.
As a result they are looking to tempt the Merseysiders with an offer which falls just short of their valuation in the hope it will be enough to push a deal over the line.