Davies spent the 2021/22 season on loan at Sheffield United, making 21 appearances for the Blades in the Championship, scoring once and earning only three cautions.
The 26-year-old has yet to feature for Jurgen Klopp following his arrival in the winter transfer window during the 2020/21 season, when the Reds faced a shortage in the heart of their defence.
Blackburn Rovers currently lead the queue of Championship clubs interested in signing the defender, offering to cover all of his wages next campaign as well as pay a loan fee.
The Ewood Park outfit are in talks with Liverpool, who are pushing to sell Davies rather than sanctioning a loan departure.
At Anfield, Davies currently finds himself behind Virgil van Dijk, Joel Matip, Ibrahima Konate and Joe Gomez in the pecking order at centre-back, and is unlikely to dislodge any of them.
Davies has not travelled with the rest of the squad for their pre-season tour of Thailand and Singapore as the Reds seek to find him a new home.
Liverpool fell agonisingly short of completing a continental quadruple last season, finishing as runners-up in the Premier League and the Champions League, but managed to win the FA Cup and the EFL Cup.