The 25-year-old hasn’t featured for Liverpool since a 3-0 victory over Tottenham Hotspur at White Hart Lane in August.
Sturridge suffered a thigh injury while training with the England squad, before a calf strain extended his period on the sidelines last month.
The England international was thought to be in contention to face Chelsea at Anfield on Saturday after travelling to Madrid mid-week.
However, Liverpool manager Rodgers confirmed Sturridge is training at Melwood but require more rehab work before making his comeback.
“He’s out on the field today with the rehab team, he was moving very well,” the Northern Irishman said at the training ground. “But he’s probably a little bit of time away.”
Sturridge scored 21 goals in 29 Premier League games last season.
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