The 26-year-old, who was left out of Juve's Champions League squad for the group stages of the competition, has only made eight Serie A appearances during the 2019-20 campaign.
A number of clubs, including Manchester United and AC Milan, have previously been credited with an interest in the Germany international.
However, according to The Mirror, Everton are now very much in the hunt for the midfielder and are preparing to launch a £30m offer in the hope of completing a January deal.
The report claims that now Toffees boss Carlo Ancelotti wanted to sign Can when he was in charge of Napoli and views the midfielder as the ideal signing to boost his squad.
The former Bayern Munich youngster made 166 appearances for Liverpool between 2014 and 2018 before running down his contract at Anfield to join Juve on a free transfer.body check tags ::