Liverpool veteran Carragher convinced of joining title battle
Carragher remains clear on the club's overall objective this season but feels it is too early to have definitive targets.
He told liverpoolfc.tv: "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.
The best of the derby win in 15 minutes
"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 we want to win the league.
"I always change my opinion of what I want us to do, considering where we are. At this moment people are saying we are in a race with Spurs and Arsenal because we are a little bit away from City and Manchester United.
"But if we can catch them up over the next month or so (who knows). We play Manchester United next, so if we can get three points there, and then against City and Chelsea - you can change your opinion."