Sturridge has picked up where he left off in the spring, scoring winners in each of Liverpool's first two Premier League games to add to his six in five matches at the end of last season.
But Rodgers reckons there is more to come from a player still capped just six times by his country.
"If you look at Daniel Sturridge and what he has, as long as he continues and keeps his fitness, he would be a big threat for any team," the manager said.
"You'd look at him and people would think he'd maybe be a Brazilian striker with his body physique and his pace and power.
"England are fortunate to have him because he's a big talent but he knows he needs to be consistent, he needs to get himself the games and the goals. I have got no doubt, though, that he will be a massive asset for England.
"It's about consistency. Strikers are judged on goals in games and if you judge him on that his record's very good.
"But it's still very early, he has a lot more to do, but there is no question he's potentially the top English striker. He's got all the tools to be that.
"The frightening thing is he's still got a bit to go in terms of his fitness. He missed nearly all of pre-season and he only joined the group in the last few weeks.
"I think that once he's fully fit then he'll be even better. We've taken all the pressure off him and it's just about him working hard. When he does that you see all his qualities and at the moment he's working very well."
Sturridge's form has helped Liverpool make light of Luis Suarez's ongoing suspension, but Rodgers is still aiming to add to his squad before the transfer window closes next week.
Speaking at a press conference ahead of Tuesday's League Cup tie with Notts County he said: "We'll hopefully come out with a stronger group.
"I've got every faith, even if we didn't get any more in, that these players will do really well for us this season, but the idea is to strengthen that little bit more and hopefully we can do that."