The 21-year-old moved to City from Everton in the summer, but has managed just six appearances so far due to a spate of injuries.
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"It will probably be another few weeks, so I'm looking into the New Year. I'm doing quite a lot of training at the minute though, so I'm keeping busy," he told the club’s official website.
"It's down to strengthening now, so I'm doing a lot of work in the gym and am just getting it right to prevent another injury.
"It's been a frustrating start to the season and to my City career, bit I'm focused now and I'm ready to get back."
Rodwell will miss games against Reading, Sunderland and Norwich, and depending on his comeback date could also miss matches versus Stoke, Arsenal and Fulham.