Citing Italian newspaper Corriere dello Sport, the MailOnline's Will Griffee said the Old Lady will make a "last-ditch move for their top transfer target" and are aware that time is running out before the start of the Premier League season.
Griffee added Liverpool could be tempted by a significant offer as Can's current Reds contract expires next summer, but the Anfield outfit may also "err on the side of caution" given the ongoing speculation surrounding Barcelona target Philippe Coutinho.
Given Jurgen Klopp's Liverpool side finished in the top four of the Premier League for the first time since 2013-14 last term and are just a play-off victory away from the UEFA Champions League group stages, positivity should currently be prevalent at Anfield.
However, there are unquestionable nerves they could lose Coutinho, one of their best players, to Barca as a replacement for Neymar:
And given the current situation, it is unlikely fans of Liverpool would be happy to see Can, 23, depart.
The Germany international moved to Liverpool from Bayer Leverkusen in 2014 for £10 million.
He has since become a key part of Klopp's side, making 32 Premier League appearances for Liverpool last term and improving with every game.
As such, it is little surprise Juventus are interested in signing him but, by the same token, it is likely Liverpool will not want to let him go.