The England international, who moved to Anfield from Chelsea back in January, scored an impressive 11 goals in 16 games for the Reds and also made five assists in all competitions.
And Liverpool’s all-time top goal-scorer Rush believes that the 23-year-old will become one of the Reds’ key men next term as they look to secure a route back into the Champions League.
“Sturridge can get even better without a doubt,” Rush told Liverpool’s 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, [Philippe] Coutinho has as well – some of the passes he put through were absolutely superb.
“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.
“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.”
MORE: The latest football news