The 25-year-old England international had surgery in New York on Tuesday in a bid to cure a number of related problems with his thigh and calf which have seen him make just eight Premier League starts this season.
"We anticipate that Daniel will be back, hopefully to train around about September," Rodgers said.
"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."
Rodgers was asked whether, with the time it would take for Sturridge to get back to proper match fitness, the chances were they were unlikely to see the best of the striker until November.
"It is not just about fitness but football fitness, and that takes a bit of time," he added.
"The important thing will be to let him recover, work hard in his rehab and we have great support from our owners in that he is able to go to the world's leading specialists in America.
"He will work very hard to get back fit and the sooner the better for us."
