Davies has received a lot of interest given his Preston contract expires in six months, including from Sheffield United.
Celtic have been monitoring Davies for some time and he was a target for the Scottish Premiership side during the previous transfer window.
Davies, a left-footed centre half who can also play at left-back, is a product of Preston's academy and enjoyed loan spells at York City, Tranmere Rovers, Southport, Newport County and Fleetwood Town, prior to breaking into the Lilywhites' first-team on a regular basis during the 2017/18 season.