This is according to The Guardian, who report that Reds boss Brendan Rodgers - aware of his current squad's defensive deficiencies - is keen on the addition of a new left-sided defender, with Bertrand topping his wishlist.
24-year-old Bertrand would presumably prove an attainable target, with the England international never having managed to successfully establish himself as a first-team regular at Stamford Bridge.
Traditionally the chief understudy to Ashley Cole, Bertrand figured somewhat more prominently for Chelsea under the respective reigns of Roberto di Matteo and interim manager Rafael Benitez.
However, Bertrand has been afforded few opportunities to impress since Jose Mourinho returned for his second stint as Chelsea boss last summer.
Eventually sent out to Aston Villa on a loan deal until the end of the 2013/14 campaign, the former Reading and Nottingham Forest man made 10 appearances for the struggling Villains, helping Paul Lambert's side to retain their Premier League status.
Liverpool's need for a new left-back is obvious, particularly with Spaniard Jose Enrique having missed most of the season through injury.
Young Jon Flanagan - often preferred to Aly Cissokho - coped very well indeed with switching to the left-hand side towards the end of the campaign, but it seems incredibly unlikely that Rodgers will expect him to player there on a regular basis.
A possible switch to Liverpool for Bertrand would presumably provide a boost to his international prospects, with the player not having been considered by many as a viable defensive option for England at the upcoming World Cup in Brazil.