The England striker was ruled out for up to three weeks after returning from international duty with a thigh injury.
Liverpool missed Sturridge badly in last week's home defeat to Aston Villa, and barely coped without him as they scraped past Ludogorets in the UEFA Champions League on Tuesday.
The 25-year-old is sidelined for Saturday's trip to West Ham, but Rodgers feels he may be fit for next week's clash with Everton at Anfield.
"Daniel is doing well and is out on the field doing some work," Rodgers told the Liverpool Echo.
"He should hopefully be back training at some point next week and will have a chance for the derby."
Sturridge scored 21 goals in his first full Premier League campaign with Liverpool last season as Rodgers' side finished second behind Manchester City.
