Reds boss Jurgen Klopp has been a long-term fan of Demirbay and admitted his admiration last year.
BILD says he remains keen on the midfielder this season and has had him watched in Champions League action this season.
Asked about the interest, Demirbay stated yesterday: "Of course I can handle that."
Demirbay was outstanding for the 4-0 win against Stuttgart and coach Julian Nagelsmann enthused: "He gets from me an A1 grade with a star. He was certainly the key player in the second half."