The German midfielder has become a top target for the Bianconeri.
Liverpool have rejected the latest bid from the Old Lady worth 25 million euros, according to Mirror.
The 23-year-old is rated highly by Juve head coach Allegri as he seeks to bolster his squad ahead of the upcoming 2017-18 campaign.
Can’s contract will expire at the end of the season and Juventus hoped they could lure him to Turin for a fee of €25m.
However, Mirror report that the Reds from Anfield have turned down the offer even though the German is yet to sign a new contract.