The former Liverpool legend is delighted by the striker's "absolutely incredible" start to life at Anfield, and believes the 23-year-old can help bring success back to Merseyside
The England international has scored 11 goals in just 16 appearances for the Merseyside club since moving from Chelsea for £12 million in January.
Rush's 346 goals for the club make him the Red's highest goalscorer, but the Welshman believes Sturridge has it in him to become another Liverpool legend.
"Sturridge can get even better without a doubt," he told the club's official website.
"He's got some great skill and with a good pre-season I think you will see an even better Sturridge next season.
"He needs to get fully fit. He was absolutely incredible in some of the games. He has got a good football brain, Coutinho has as well - some of the passes he put through were absolutely superb."
Rush, who scored 346 times for the Reds, believes the current squad has a host of match-winners and is hoping for a successful campaign next term.
"When you've got the likes of Coutinho, Sturridge, Luis Suarez, Steven Gerrard and people like that you have got four or five people who can win your games when previously we only had one or two," he added.
"Sturridge has had a couple of little injuries but if he can get fully fit and get through the pre-season then I think there are exciting times ahead.
"We know we can keep clean sheets. We are an attacking team who do create a lot of chances but it's all about putting them away."