With Trent Alexander-Arnold leaving Liverpool when his contract expires at the end of June, they need to find a new right-back signing.
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Sky Deutschland says Liverpool are focusing on Frimpong as a direct replacement.
The Reds hope to sign the Holland international for a fee in the region of £30m. Talks between Liverpool and Frimpong are now at an advanced stage over personal terms.
And Frimpong has previously said that "Liverpool is a great club with history", when asked about past transfer speculation.
With Bayer, he has 189 appearances, scoring 29 goals and making 44 assists.