The Anfield outfit had a £16million bid turned down in May, and were unwilling to up their offer to around £20million, and with Guilherme Siqueira's move to Atletico Madrid completed earlier this summer, manager Brendan Rodgers has now earmarked his former Swans defender Davies.
A reported move for Ashley Cole failed to get off the ground, and the former England defender joined Serie A side Roma this week, as yet another reported target bit the dust.
Meanwhile, Chelsea continue their spending after agreeing a deal to bring Brazilian full-back Luis to Stamford Bridge, and the defender arrives in London with a burgeoning reputation after playing his part in one of the finest defences in Europe en route to landing the La Liga title.
The move for Luis is in stark contrast to Liverpool's continued struggles to attain the services of a top-class left-sided defender.
Jose Enrique was signed in 2011, and while the Spaniard is a dependable operator, he spent most of last season on the sidelines and made just eight appearances.
Aly Cissokho was unable to adapt to the rigours of Premier League football following his loan move from Valencia and Jon Flanagan was forced to play the final few months of the season at left-back, despite being primarily a right-sided player.
His adaptation was admirable, but the truth is, the left-back slot has plagued Liverpool for years, with a procession of players unable to make the spot their own for one reason or another.
John Arne Riise perhaps filled the spot with the most distinction from 2001-2008, and Fabio Aurelio was a technically gifted operator - when he was fit enough to take to the pitch.
However, fans still shudder at the likes of Emiliano Insua and Gregory Vignal's displays on the left side of defence, and that's before we even mention Christian Ziege, Paul Konchesky, Andrea Dossena and Djimi Traore.
Reports circulated on Tuesday evening that the Reds had been rebuffed in their attempts to land Davies, with an £8million offer turned away by the Welsh club.
And as Chelsea begin to put the finishing touches on their big-money move for La Liga winner Luis, the labouring attempts to sign a left-back of their own have become all the more glaring for Liverpool.