The 25-year-old centre-back’s future at Preston has come under the scanner due to interest from both sides of the border and his contract is due to expire in the summer.
Celtic have been linked with Davies, but it has also been claimed he has interest from the Premier League in the shape of Sheffield United.
Chris Wilder wants to bring in a defender and he is said to be keen on signing Davies from Preston in the ongoing transfer window.
But it has been claimed that a deal is unlikely to happen and Davies is not expected to move to Bramall Lane this month.
Sheffield United are still interested in bringing in a centre-back but the Preston defender is not likely to be their man in the January window.
The news will be welcome for Celtic as it removes potential competitors for the 25-year-old Barrow-born stopper.
Celtic manager Neil Lennon wants to strengthen his defence, which has struggled this season and is a key reason behind the Bhoys being 19 points Rangers in the title race.
Davies has been looked at a possible solution and the Glasgow giants are considering making a move for the Championship defender.