The 25-year-old has been sidelined by hip and thigh injuries this season and has not played since the FA Cup quarter-final win over Blackburn Rovers on April 8.
England international Sturridge underwent surgery in the U.S on Tuesday after only playing 18 games in this campaign, scoring five goals, compared to 33 appearances last season and 24 goals.
"We anticipate that Daniel will be back, hopefully to train around about September," Rodgers told a news conference.
"Obviously it is long period of time out but we hope the problem and issues have been resolved with the operation.
"We hope he is available to train in September and then it is about getting his fitness in.
"He's been a big miss for us. Once he's fully fit he can be a key player for us."
Rodgers has made no secret of his desire to bring a new striker to the club after Sturridge's injury-hit season but the Liverpool boss said he was not interested in Manchester United-bound Dutch forward Memphis Depay as he has "other priorities."
Fifth-placed Liverpool travel to Chelsea on Sunday hoping the newly crowned Premier League champions are suffering from a hangover after winning the title for the first time since 2010 last weekend.
Rodgers has still not given up hope of snatching the final Champions League qualification spot but Liverpool trail fourth-placed Manchester United by four points with three games remaining.
"Chelsea were the deserved champions, but that doesn't take away what we are looking to do. We are looking to finish the season strong," Rodgers said.
"All we can do is look to win our last three games and see where it takes us. If Chelsea have had a few days off they deserve it.
"The players are very motivated. This is a wonderful bunch of players to work with. It has been a tough season and the team is committed to moving the club forward."
(Reporting By Michael Hann; Editing by Amlan Chakraborty)
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