Last season was a transitional one as the Northern Irishman began to implement his vision at Anfield.
It was an inconsistent campaign with some positive displays which saw the Reds finish seventh.
However, Sturridge, who had an immediate impact on his arrival in January for £12million and provided some much-needed support up front, is encouraged by his five months under Rodgers.
"With the philosophy that the manager has we should be challenging for honours," said the England international.
"I think it's going to be great for us in the future and we can move forward.
"I think we did things last season, both prior to me coming here and then with my help, to deliver some better statistics than we have had in previous years in terms of goals and attacking play.
"It's exciting to be part of that philosophy and the new regime that the manager is forming for us to move forward as a club."
Sturridge's first 10 goals for the club were the quickest in the Premier League for Liverpool and gave the side impetus at the turn of the year.
He hopes to be able to maintain that form when the new season kicks off next month, especially with Luis Suarez suspended for the first six matches if he is still at the club by then with doubts persisting over his future.
"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," he told the official monthly LFC magazine.
"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."