Liverpool continued to build on their good early season form with a 4-1 home victory over West Brom last weekend to keep them two points behind league leaders Arsenal in third place.
And Cissokho insists the Merseysiders can make a statement of intent if they can pull off a victory over Arsenal this weekend.
"I think if we could get the three points against Arsenal it would send a strong message to the other teams in the competition," said the Frenchman.
"We'll take it one match at a time but we have started well and we are near the top of the league, although there will be difficult matches.
"The tough ones can be against the lower teams in the league, where you might think of having a more relaxed outing.
"But if you're setting out to qualify for the Champions League through a domestic league like the Premier League you really have to concentrate and remain serious for each match, whether it's against a team from the lower end of the table or one right at the top.
"We're only a couple of weeks ahead of the international break, so it would be good to take the three points at Arsenal, and look forward to the next home match and try to stay at the top of the table during the break."
The Valencia loanee says Liverpool's senior players will be vital ahead of Saturday's game and insisted the club remains one of the biggest in world football.
"We have players in the squad like Kolo Toure, Steven Gerrard, Daniel Agger and Martin Skrtel, who have plenty of experience and who have started in some big European matches as well," he said.
"We are at one of the biggest clubs in the world and they motivate everyone."