Davies, 25, will undergo a medical in Liverpool on Monday before completing the transfer, which also includes Anfield youngster Sepp van den Berg, 19, moving to the EFL Championship club on loan until the end of the season.
Liverpool manager Jurgen Klopp has been pushing the club's recruitment team to sign a centre-half during the transfer window after losing both Virgil Van Dijk and Joe Gomez to long-term knee injuries earlier this season.
Captain Jordan Henderson has played in defence in recent weeks, including Sunday's 3-1 win at West Ham, with fellow midfielder Fabinho also being forced to drop into the back four due to the team's injury crisis.
Preston defender Davies has made 19 appearances in the Championship this season and played in the weekend defeat at Sheffield Wednesday.
And although he is unlikely to be thrust straight into the Liverpool team for Wednesday's Premier League clash with Brighton, Davies will give Klopp much needed cover at the back if, as expected, Liverpool complete the deal before Monday's transfer deadline.