The 25-year-old is out of contract this summer and has been linked with both halves of the Old Firm.
One report this week claimed Gers were ready to step up their interest and were piecing together a pre-contract offer which would see him join Steven Gerrard's side at the end of the season.
But it appears the Light Blues boss will be looking elsewhere after a Gers insider insisted the runaway Premiership leaders had "no interest" in the left-sided centre-back, according the PA news agency.
That will come as a huge relief to Deepdale boss Alex Neil, who has reportedly offered Davies a club record contract worth £17,000 a week in a bid to tempt him to sign on again with Preston.
Rangers have also been linked with a move for Airdrie youngster Thomas Robert.
The highly-rated 20-year-old - son of former Newcastle winger Laurent Robert - stunned Scottish football back in the summer when he knocked back offers from clubs in Germany, England and a new deal at former club Montpellier to sign for the League One Diamonds.
But Rangers have ruled themselves out of the chase for his signature, with the Ibrox source confirming the Frenchman is not on Gerrard's list of targets.
Gerrard has, however, confirmed he is close to securing Aberdeen winger Scott Wright on a pre-contract but there has been no developments on talks with the Dons which could potentially see 23-year-old make his move to Glasgow this month.