Van Dijk dismissed any hints, primarily from neutrals, assessing a daunting fixture schedule that an early Champions League exit could help Premier League ambitions.
"I don't think they are Liverpool fans if they are saying that," said the Dutchman.
"I definitely look at the squad and think it can compete on two fronts. We still need to show it.
"We want to compete on the highest level. We are top of the league, but it could change next week. The main thing for us is to do everything we can to go through. I am very confident in my team."
For Klopp, the tone of such games is set in the Uefa briefing. This is where he is most effervescent before the most meaningful dates, talking excitedly about the possibilities, displaying the dynamism he expects from players and fans.
"I know it will be difficult but I cannot help but think about it with a smile on my face," said the German manager.
"We are in a good moment for weeks and months as a club and a team. We have to use it. We do not need to make it any bigger than it is, but it is big.
"That is exactly how we want to take it as an opportunity. The boys are desperate to stay in the competition. They have grown. They have got better and better, but we were not 500 times in a situation where 1-0 is good but 2-1 is not, 3-1 is good again, but 3-2 is not.
"It is a mix of being really lively and making an emotional game of it. It must be. The crowd can be really emotional from the first second. They do not have to wait for anyone else. They can start before the game if they want. Then we will see what we are doing on the pitch.
"We struggled a lot in Napoli with their build-up. From that point of view, it was the worst game for us since I don't know when. It was just not good that night, and in the end, they could use it in the last second. That is all our responsibility.
"We need to be really active, focused, in the game. They should have to work hard for any chance and then we still have the opportunity to save it. On the other side, we have to score. The only thing that is clear is, if we go 1-0 up, then it is not like it would usually be at 1-0. If they score, we then have to score a second and a third and that is a hard job to do. We have to do the job."
Dejan Lovren is likely to return to the side after missing the past three matches with concussion. Captain Jordan Henderson could also come back into midfield after being a substitute against Bournemouth on Sunday.
Carlo Ancelotti has enough Anfield experience to ensure the Italians do not succumb to the noise as Roma and Manchester City did last season. Ancelotti won as both Chelsea and Real Madrid manager in the stadium.
"We all know about the intensity they play in these games," said Ancelotti. "We haven't come here to sit back, we've come here to play our own game.
"I am not too sure what Liverpool will be setting out to do, but I know what we will be aiming for. We can draw on the first game in Naples [a 1-0 win for Napoli in October], it has given us a lot of confidence, and we'd like to put in a repeat performance.
"I hope my players are positive, as they want to play in one of the best stadiums in the world in terms of atmosphere."
