QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
The Frenchman made the move to Anfield in the summer on a year-long loan deal from Valencia, providing competition for Jose Enrique at left-back.
He is enjoying life at the club and intends to keep working hard to ensure he has a chance of staying beyond the end of the season.
"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," Cissokho told Liverpool'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.
"It's a great city. We have a great training complex here, and we all have a lot placed at our disposal to get the best from each player, and that's a good thing for me."
Cissokho appreciates that he faces a challenge to establish himself as a regular starter under Brendan Rodgers, but he is relishing the physical nature of English football and is ready to play his part.
He said: "To start with, when you want to play in a team like Liverpool, you have to expect that there's going to be high level of competition for each place, whether in central defence, midfield or in attack.
"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.
"I'd say the English championship resembles the leagues I've known to date - very physical, high tempo, as in France, and like in Spain and Portugal, a lot of intensity, as with here, combined with technical football.
"It's very engaged, and it's non-stop. It's surprising to see that even with those teams in mid-table, as well as those nearer the top of the table, there's never a let up in the tempo, and they all play at the maximum level right up to the last minute of the match."