The Reds finished seventh in the Premier League during Rodgers's first season in charge, with Sturridge adapting quickly to life at Anfield following a January switch from Chelsea.
Sturridge believes that Liverpool must always strive to challenge at the top of English football, while remaining adamant that his squad are building towards title contention thanks to the style implemented under Rodgers.
He told the club's official magazine: "We'll all be doing everything in our power to make sure that Liverpool is a club that is challenging for Premier League titles because the fans have been waiting for that for a long time and hopefully next season we'll be in the running.
"When you play in the Premier League, everybody's goal is to lift that trophy, to have the celebrations and to know that you've succeeded and been a champion over everybody else in the division.
"So the main aim for next season and the seasons ahead is to try and help the team do well in the Premier League. I'm sure with the philosophy that the manager has, we'll be able to do that."
The 23-year-old scored 12 times in 16 appearances for the Reds last season, finishing the campaign in style with a hat-trick against Fulham.