Liverpool signed Davies after injuries to Joel Matip, Virgil van Dijk and Joe Gomez left them short of centre-backs at the start of 2021.
The 26-year-old failed to clock a single minute of game time under Jurgen Klopp following his arrival and with all the first-choice centre-backs back from injury as well as the arrival of Ibrahima Konate at the start of the 2021/22 season, that was unlikely to change.
Davies spent last season on loan at Championship club Sheffield United, making 21 appearances, scoring once and getting cautioned only on three occasions.
Having completed a permanent move to Rangers this summer, there have been questions about how much the Gers were paying him given suggestions he was earning as much as £60,000 per week while at Anfield.
However, it has been pointed out that Davies was never on that kind of money at Liverpool and Rangers will pay him less than half that reported sum.
Left-sided defender Calvin Bassey, who can play at both centre-back and left-back, left Rangers for Ajax this summer in a club-record sale recently.
Davies will be expected to shoulder part of the burden of replacing Bassey, with interest in signing Besiktas’ young left-back Ridvan Yilmaz also shown by the Ibrox outfit.