The 23-year-old, who has resisted offers to extend his deal with the Premier League side, will be out of contract at the end of the season.
Massimiliano Allegri has tracked the German throughout the transfer window, with the Bianconeri eventually having accepted that the Reds have no intention of selling Can now.
Liverpool boss Jurgen Klopp, who has already enhanced his options in the centre of midfield for 2018-19 by signing RB Leipzig dynamo Naby Keita, has admitted the "situation is not perfect".
He would have preferred to have already secured a long-term commitment from Can, but the 50-year-old "is still positive we can find the right solution for both sides".
Klopp also revealed that it is "clear we want him and he also wants to stay" and that "it is about a few little details".
Juve believe Can would be a shrewd acquisition for them and want to ensure they are in pole position to recruit him should he continue to reject Liverpool’s terms.
Sources at the Serie A club have, however, dismissed reports that a pact has already been made, saying such claims are premature.
Meanwhile, as revealed by Goal last week, Crystal Palace are working on a structured deal to sign Mamadou Sakho.
The centre-back has long agreed personal terms with the Eagles, having enjoyed an influential loan spell at Selhurst Park last season.
Liverpool are willing to accept achievable add-ons to reach their £30 million valuation for the 27-year-old.
West Bromwich Albion, Leicester and West Ham have all been linked with approaches for the Frenchman, but his preference has been to return to Palace.