Liverpool sit nine points off fourth-placed Tottenham Hotspur with 13 games remaining, but have taken encouragement from their recent 2-2 draws at Arsenal and Manchester City.
Brendan Rodgers' side were the better team for long spells in both of those games and Suarez is delighted with the progress being made by the Reds.
"I'm very pleased and very happy because Liverpool is growing," Suarez, who has scored 17 Premier League goals this season, 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 in to 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."
Suarez has been linked with a summer move to Bayern Munich and, when asked if Liverpool should talk about his future in the summer, he said: "Yes, we should talk this June or the next one, in 2014. My contract ends in 2018.
"I'm very happy here and my family love the life here too.
"I want to enjoy being at this club where I, like all the kids, dreamed of playing and now I'm fulfilling that dream."
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