Rodgers's first year in charge of Liverpool saw the Reds finish in a disappointing seventh place, although their form towards the end of the season raised optimism around the club that has continued into the current campaign with two wins from their opening two games.
The Anfield club are expected to challenge for a top-four spot and therefore qualification for the Champions League this season, but Rodgers believes that his side should eventually be aiming even higher.
"We're not entering the league just to be fourth. Winning the league is about the best team not just the best players. That's our challenge. It's important for Liverpool to be up there; I think it's important for football for Liverpool to be there because this is one of the biggest clubs in the world. But it doesn't give you a divine right," Rodgers told BBC Sport.
"We obviously had a hard start last season in terms of games, and the players coming back late to pre-season. That took us a wee bit of time to get going. But from the turn of the year, since January, we've been very strong. We're getting that consistency back.
"This year is a big year for us. I signed here for three years and the objective was, certainly in the third year, to be somewhere near challenging for the Champions League."
Liverpool will look to continue their 100% start to the season when they face fierce rivals Manchester United at Anfield tomorrow.