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.
“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.
“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.”
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