Liverpool have agreed a £2 million fee with the Championship club for the 25-year-old, and he is set to undergo his medical with the reigning champions soon.
Preston have also registered an interest in taking Liverpool's Sepp van den Berg on loan for the remainder of the season.
The club's long-serving chief executive, Peter Lawwell, announced on Saturday (AEDT) he will be stepping down at the end of the season, but the pressure is building on him to make a change and salvage second in the league and a place in next season's UEFA Champions League qualifiers.
Concerns over getting overseas targets into the country amid Covid-19 restrictions were also a consideration as Liverpool made the move to sign Davies.
This comes as a big frustration to the Celtic support in particular after believing that we would be securing a player who we have supposedly been targeting since the summer.
Ben Davies playing for Preston
"I'm not sure there's an £80m centre-back available at the moment, or pretty much I know this", Klopp told a press conference. "It's about solutions and that's what we are working on".
"So sort the problem we have now, that is how we do it usually".
"And if they need money then they want insane money".
Given the club have had since January 1st to agree a pre-contract with Davies, there's little excuse for their inaction too, unless the player wanted to survey his options.
"As a football fan you can sit at home and think "They have to do something". We see the situation.