Reports in Spain suggest Brendan Rodgers will look towards other left back targets in the summer, dependent on the recovery of Jose Enrique.
Cissokho arrived last summer on a season-long loan from Valencia, but has not impressed enough to earn a permanent deal for the Champions League chasing side.
Rodgers will now look to provide cover for first choice Enrique, who has not featured for the Reds since October.
Cissokho never really got going at Anfield, after picking up an injury that ruled him out for six weeks in just his second appearance for the club.
He has since been competing with natural right backs Jon Flanagan and Glen Johnson for a starting place, and in recent weeks has found himself back on the bench.
The Frenchman had previously been positive about his future, revealing he was enjoying his time and would be open to stay should Liverpool look to activate the option to sign him for £3.3million in the summer.
“I have given my very best for Liverpool and we will see at the end of the season what both clubs will decide,” Cissokho said.
“If I have to leave Liverpool, I will leave. I am doing a nice job and that is the most important.”