The club could only muster a seventh-place finish last season in manager Brendan Rodgers's first campaign in charge at Anfield.
"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," Sturridge told the club's official magazine.
"So the main aim for next season and the seasons ahead is to try to help the team do well in the Premier League. I'm sure with the philosophy the manager takes we'll be able to do that."
Sturridge, who joined the Reds in January from Chelsea, is expected to be fit for the start of the season after suffering an ankle injury while on international duty with England.