Both Liverpool and Manchester United have expressed an interest in the Lyon defender in the past and were linked with a move for him in the January transfer window.
While a deal failed to materialise Liverpool are ready to renew their interest this summer, but they face competition from Napoli for the 24-year-old.
TalkSPORT suggests, quoting reports in France, that Cissokho is ready to quit Lyon this summer and sign on the dotted line abroad, and with United reportedly in talks over a deal with Everton for Leighton Baines, Liverpool will go head to head with Napoli for his signature.
Liverpool can call upon the services of Jose Enrique at left-back but are said to be in the market for cover for the Spaniard, whose performances tailed off fairly dramatically towards the end of the season.
Lyon will demand around £6 million for Cissokho this summer, a fee which should trouble neither Liverpool or Napoli.