With the temporary spell having come to an end, the 26-year-old would have been a player whose situation United’s recruitment department will have kept a close eye.
Davies was solid if not spectacuar during his time at Bramall Lane but is certainly a player who should at least be playing at the top end of the Championship.
However, if reports from Liverpool are to be believed then the price will more than likely put off United.
The Liverpool Echo state that an 'overall package worth around £4m' would have to be stumped up to prise the player away from Anfield.
Celtic, who recently secured former Blade Cameron Carter-Vickers on a permanent deal following a loan spell from Tottenham last season and remain on the look-out for another defender, are understood to be interested in signing Davies having attampted to bring in the player before he made the move across Lancashire to Merseyside.
Middlesbrough, whose boss Chris Wilder was in charge of United when the Blades first attempted to sign Davies from Preston, are also reportedly keen on the player.
Davies made 23 appearances for United last season in a campaign that was punctuated by injury and illness.