The Reds currently sit seventh in the Premier League table but are just nine points off fourth-placed Tottenham Hotspur.
The 25-year-old had been linked with a move away from the Merseysiders in order to play in Europe's elite competition, but Suarez is confident that Liverpool can bring Champions League football back to Anfield.
"I'm very pleased and very happy because Liverpool is growing," Suarez told Marca.
"It's not the team that it once was as they have had a dip. But now we have a new coach who has a philosophy of the game with which the players are very happy.
"The only thing missing is to have more positive results so we can finish in a Champions League spot. We showed we can match anyone - we had chances to win many of those matches. If we go into every game in the Premier League with the same intensity that we've shown in the big matches we can be much higher in the table."
Liverpool's last Champions League appearance came in a 2-1 defeat to Fiorentina in December 2009.