The England striker has impressed in Liverpool's pre-season matches, however, scoring in a 4-1 win over Manchester United on Sunday that prompted manager Juergen Klopp to say that Sturridge would have a role to play at the club "if he is fit".
"The hunger will never change. I'm taking every day as it comes with a positive mindset. That's all I'm going to do," Sturridge told reporters.
"Pre-season has been going great but, you know, I'm not getting too carried away. It's just great to be part of the club and helping and making sure that we can win games.
"I just want to help the team win something ... We have been close before a lot of times. I wasn't here for last season's Champions League (final) but it was so close, so close.
"We want to win something."
Liverpool face Italian sides Napoli and Torino in their remaining pre-season fixtures before kicking off their Premier League campaign against West Ham United on Aug. 12.
(Reporting by Ankit Ajmera in Bengaluru, editing by Nick Mulvenney)
