The club are off the pace in the Premier League but the defender believes his team should be taken seriously.
“At the start of the season you have the idea of winning the league, but in the last few years we’ve finished sixth and seventh”, Carragher told Liverpool’s official site.
“For us to get into the top four we’ll be pleased with that this season.
“But if it gets to Christmas and we are only three points behind Manchester United or Manchester City, we are going to say that we want to win the league.
“I always change my opinion of what I want us to do, considering where we are.”