The 26-year-old left North End in the January transfer window after sealing a dream Premier League move to Liverpool.
However, he has not played one minute of football for Jurgen Klopp's men and looks set to move to Bramall Lane.
It is understood the Blades will have no option to buy as the Reds look to keep their options open regarding the future of the centre-back.
Celtic, Bournemouth and Burnley have been interested in the 26-year-old.
Davies joined North End as a youngster and went on to make 145 appearances, becoming a mainstay of the Lilywhites' defence in the Championship.
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