Over the past week, Werner has twice talked up the prospect of moving to the Reds this summer.
After victory over Schalke on the weekend, the striker enthused: "We have there the best coach in the world with Jürgen Klopp, who is German. There are many things that would suggest that my style of play might fit well. Now inquiries come in, you don't have to lie."
BILD says RBL management are calm over Werner's comments, with no approach from Liverpool yet fielded. Klopp also hasn't spoken to any RBL officials in recent weeks.
Werner's current deal carries a €55m buyout clause which carries a deadline to the end of April.