Liverpool swooped to snap up Davies in the January transfer window from Preston North End, but he did not play for the Reds last season.
With Liverpool now having Virgil van Dijk and Joe Gomez back at full fitness, Davies could be sold in the ongoing summer transfer window and Sheffield United have been heavily linked with him.
However, the Blades have not yet gone beyond an enquiry for the centre-back.
The Championship side will have to turn their interest into a bid to try to take Davies to Bramall Lane if they want to snap him up.
Liverpool are cashing in on fringe players as they look to raise funds to spend on new signings and Davies could be sold.
Reds boss Jurgen Klopp has a host of options in the centre of defence and Davies could be looking at limited game time if he stays at Anfield.
Sheffield United kick off their Championship campaign next weekend against Birmingham City.