The Reds are in the market for a new right-back after it was finally confirmed that Trent Alexander-Arnold will be leaving the club as a free agent this summer.
According to Sky Sports, Frimpong has told Leverkusen he wants to leave and would be very keen to make the move to Liverpool at the end of the season.
With a release clause in place and Frimpong happy to join, it is said that a deal could be swiftly completed if Liverpool do decide to focus their attention on the Dutchman.
Reports in Germany earlier this week suggested that a deal was close to being wrapped up, with an agreement set to reached for Frimpong to sign a five-year contract.
He has made 47 appearances this season, chipping in with five goals and eight assists for Xabi Alonso’s side from wing-back.
Frimpong also played a crucial role last season as Leverkusen went unbeaten on their way to sealing the Bundesliga title.
If his release clause is activated, Celtic will earn in excess of £5m from the deal, having inserted a 30% sell-on clause in the deal when selling to Leverkusen for £11.5m in 2021.
Speaking last year about his future, Frimpong said: "Liverpool is a great club with history. That would be great. Who knows what the future will bring."