Karius is coming to the end of a two-season loan with Besiktas, where they're expected to pass on the option of signing him permanently.
The German has little chance of re-establishing himself at Anfield, but is interesting Hertha Berlin.
The former Mainz No1 told BILD: “I had great success in the Bundesliga and have always enjoyed it.
"It's also great in terms of sport, it has done very well internationally so far. But it also has to make sense.
"The most important thing for me is that the club absolutely wants me, has a clear vision and that both sides have the absolute will to achieve something. Above all, I have to have a good feeling about those responsible."