The 23-year-old Germany midfielder is free to sign a pre-contract agreement with a foreign club, having entered the last six months of his contract at Anfield.
Italian champions Juve have been pursuing Can for some time but Sky Germany understand he will not leave the Merseyside club in the January transfer window.
Liverpool also remain open to him signing a new contract, with boss Jurgen Klopp happy for this to come as late as the end of the season.
Can joined Liverpool from Bayer Leverkusen in 2014 for £10m and has made 154 appearances, scoring 16 goals.
Liverpool face Merseyside rivals Everton in the FA Cup third round on Friday, followed by a home clash with Premier League leaders Manchester City on January 14.