The France international signed for Brendan Rodgers' side on a season-long loan from Valencia in August and has made six appearances in all competitions, including starting the last four Premier League games in the absence of regular left-back Jose Enrique.
Liverpool sit second in the top flight after 11 games having lost just twice so far and Cissokho is enjoying every minute of life at Anfield, adding that he would like to extend his stay beyond this term.
"It's a great source of pride for me every day to be able to play with players like this and to represent a big club like Liverpool," the 26-year-old told the club's official website.
"It's a source of pride for all the coaches I had as a youth player. Of course, I am very happy to be here and I hope to stay here.
"Everyone in the team is disappointed not to be competing in European competition, and every player wants to give his best to ensure that the club is up there in the qualifying positions at the end of the season.
"The season is long, and there are a lot of matches to come.
"The coach makes, and will continue to make, his decisions, and it's important to respect them so that the team can be in the best shape each Saturday."
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