The Germany international’s contract will expire in the summer and he has rejected the chance to sign a new deal at Anfield.
Juventus have been chasing the 24-year-old since January, but he has continually told them he will not agree terms until the end of the season.
However, according to TMW, talks have now progressed and Can’s move to the Italian champions is in its final stages.
The midfielder reportedly just has a few more clauses to agree, but a deal should be completed in the next two weeks.
Can had also been attracting interest from Bayern Munich, as well as Paris Saint-Germain and Real Madrid.