The 25-year-old centre-back has been tipped to leave the Championship club before the window closes on Monday.
The defender has suitors in the Premier League and several clubs are tracking his situation, due to his contract expiring in the summer.
Celtic are looking to lock Davies down to a pre-contractual agreement and then negotiate a fee to sign him from Preston this month.
However Burnley, who had an offer for Collins turned down by Stoke recently, could potentially decided to become involved in the chase for Davies’ signature.
Celtic lead the way though and are pushing hard to do a deal quickly, which would take any potential hijacking of the swoop out of the picture.
The Bhoys’ defence has been their Achilles’ heel this season and Neil Lennon is keen on signing a centre-back.
And it has been claimed that the Bhoys are pushing the envelope to take Davies to Parkhead in the coming days.
