The Reds did not participate in any European competition this season, after finishing eighth in the Premier League and losing in the Europa League final to Sevilla.
Klopp’s men are currently fifth in the league and in the race for a top four place.
The German, who led Borussia Dortmund into the Champions League, told The Liverpool Echo: “Things that I don’t have, I don’t miss.
“But of course I enjoyed being in that competition a lot and that’s where we want to be.
“To achieve that we need to qualify. We didn’t qualify this season. We are working to go there as soon as possible.
“We saw this week again what a strong competition the Europa League is too. Strong teams, intense games.
“We enjoyed it last season, well we did until the last match day! We had some wonderful games in that competition.
“But of course the Champions League is THE competition. We want to be part of it. To get there we have to win a few games.”