The German newspaper claims the Reds are one of several clubs in for the Switzerland international, who could leave Die Fohlen at the end of this term after four years at Borussia-Park.
The reported asking price is £37m, which would be a club record for Liverpool should they pull off a deal.
Xhaka has made a total of 26 appearances for club and country this season, scoring three goals but also picking up three red cards.
The 23-year-old’s discipline is a major flaw of his, as he was shown 18 yellow cards and two reds last term.
Liverpool currently have an abundance of options in midfield, but with Joe Allen’s contract entering its final 18 months and Lucas Leiva falling out of favour somewhat, Jurgen Klopp may look for reinforcements.
The Reds completed the signing of 19-year-old Marko Grujic on Wednesday, but the youngster has returned to Red Star Belgrade for the remainder of the season.