Liverpool sit seven points behind fourth-placed Tottenham Hotspur in the Premier League table with 14 games remaining and will face competition from Merseyside rivals Everton in fifth and sixth-placed Arsenal for a top-four berth.
"If you want to know what will happen to me if we don't qualify for the Champions League, then I will say this: I have a contract with Liverpool and I am very happy here," Suarez, contracted until 2016, told British newspaper the Daily Mail.
"I will stay," added the Uruguayan, in an interview published on Friday.
Liverpool captain Steven Gerrard told British media last month that Suarez, who has scored 43 goals in 84 appearances since he joined from Ajax Amsterdam two years ago, was "comfortably" in the top five players in the world.
"Gerrard is such a good player and what he said about me I will never forget. It's unbelievable," said Suarez, who has scored 17 league goals so far this term to be one behind Manchester United's Robin van Persie.
"I get goose pimples when I hear he said that. In my country we call it Carne de Gallina. Like the skin of a chicken. That's how I feel."
Suarez lent his support to the more junior players at Liverpool after their mentality was criticised by manager Brendan Rodgers following Sunday's 3-2 FA Cup defeat by third-tier Oldham Athletic.
"The younger players here are very good and the good thing is that many of them are home grown. That means they have a passion for the club," Suarez said.
"Sometimes we play well, as good as being in the top four of the Premier League. Then other times we don't play anywhere near as well. It's just one of those things with football."
Liverpool have yet to beat any Premier League opponents higher than 11th-placed Sunderland this season.
"This year we are playing well against lower teams and are winning. Last year we were not winning those type of games," Suarez said.
Liverpool travel to champions Manchester City on Sunday.
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