The 25-year-old joined Liverpool from Championship club Preston North End in the winter transfer window of last season, but did not feature for the Reds.
With Liverpool now having Virgil van Dijk and Joe Gomez back from injuries and having signed Ibrahima Konate, Davies is likely to fall further down the pecking order.
The centre-back’s future at Anfield is up in the air as the start of the Premier League campaign draws closer and there have been suggestions that he could leave the club.
Celtic, Sheffield United and Bournemouth have been credited with an interest in Davies and it has emerged that Liverpool are open to allowing him to leave on loan.
Celtic boss Ange Postecoglou is keen to reinforce his options and the Bhoys are expected to make a number of signings between now and the closure of the window.
However, it is claimed that Sheffield United currently lead the race.
The Blades have already had an initial loan offer rejected by Liverpool this week, with Jurgen Klopp’s side unwilling to agree to an option to buy clause.
Davies is currently in England, having returned from Liverpool’s pre-season camp in Austria last month, citing personal reasons.