Despite the Reds sitting third - where they are two points off the top having lost just once in the league and possessing two in-form strikers in Daniel Sturridge and Luis Suarez - doubts remain over their ability to sustain a challenge.
But Valencia loanee Cissokho insists the Merseysiders have enough experience and quality in their ranks to see it through to the end of the season and secure a return to the Champions League for the first time since the 2009-10 season.
"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."
Cissokho believes the Reds have a core of players who will lead them through some of the more testing times.
"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 told LFC TV.
"We are at one of the biggest clubs in the world and they motivate everyone."
Playmaker Philippe Coutinho returns to the squad for the match at the Emirates having been out of action for more than six weeks after a shoulder operation.
Manager Brendan Rodgers is arguably selecting from his strongest squad of the season with only defender Jose Enrique, whose knee problem continues to be managed, and forward Iago Aspas (thigh) missing.
The centre of defence and central midfield are the two areas of main competition with vice-captain Daniel Agger unable to regain his place in a three-man backline after injury with the same applying to midfielder Joe Allen, a B£15million signing in the summer of 2012.
Rodgers insists that is good for the club, even if it does mean he has to devote more time to assuring those players not in the team they remain integral to his plans.
Some of those fringe players featured in a behind-closed-doors friendly against Wrexham in midweek and Rodgers insists he is not concerned by rumours - dismissed by the player - suggesting Agger could be looking for a way out.
"I talk with the players with individuals and as a group," said Rodgers.
"These players, players like Daniel Agger, Joe Allen, Luis Alberto, Raheem (Sterling), are working tirelessly.
"The biggest thing is identifying - and for them to recognise that you're aware of - how hard they're working and how difficult it is.
"It's something that's part of my management. Every player here for me is very important. It's also part of being a professional.
"Football is unique. Everyone talks about football being a business but I don't know any other business where you have 25 in an office but you can only pick 11 once or twice a week.
"But that's my job, that's my problem and I manage it the best I possibly I can.
"You look at some of the other squads around and you have to have players fighting so that they know when they play, they have to be at their best.
"That's something we're developing here. We've got a long way to go to get to that level, but it's certainly something that's improving all the time.
"Daniel is one that understands fully the situation and I've reassured him.
"It's going to be the whole squad that allows us to succeed and he's a player that respects the decision.
"He's fighting and waiting for that moment, and when he does get back in he'll be in there to fight to keep his place."