The French left-back has spent the current season at Anfield, where he’s frequented Brendan Rodgers’ starting XI on numerous occasions since Jose Enrique’s injury.
However, it is understood that the Reds have not been sufficiently impressed by Cissokho to pay the £3.5m fee inserted in the deal to bring him in for the long-term.
Although he has made 13 Premier League appearances, there have been question marks raised about his defensive awareness and general ability.
Cissokho has hit out at his critics and even claimed in the past that he would be keen to make the move a permanent one, but it appears that Rodgers is already planning for life without the Valencia ace.
This news further fuels talk that Liverpool will delve into the transfer market to land a new left-sided defender this summer.
Ben Davies of Swansea is the latest name to have been aligned with the Merseyside club, who may also consider deploying Glen Johnson in the role with Barcelona right-back Martin Montoya on their wish list.