The Reds currently sit third in the Premier League table, six points ahead of fifth-placed Manchester United, albeit having played a game more.
As the race for the top four intensifies, Matip believes that a club of Liverpool's stature should always be competing in Europe's premier club competition.
"Before the season I did not expect something like this, I just wanted to concentrate on the games and I did not have a target," the Reds defender told Sky Sports News. "But now we are in this position, we want to try and keep it and get more and more.
"A club like Liverpool belongs in the Champions League, so we will fight to stay or get there. With all its trophies and history, it is one of the biggest clubs, everybody knows this. Big history, big club.
"Everybody knows something about Liverpool, it speaks for itself, this is Liverpool. It is such a great club with this history. I want to play in the Champions League because then you play against the biggest teams and the biggest players and everybody will enjoy this."
Up next for Jurgen Klopp's charges is Sunday's league trip to West Bromwich Albion.