Midfielder Adam Lallana is recovering quicker than expected from a calf injury and full back Glen Johnson is also nearing full fitness as Liverpool seek to maintain their recent improvement when they visit Aston Villa in the Premier League on Saturday.
Sturridge, who scored 25 goals for Liverpool in all competitions last season, grabbed the winner in a 2-1 win over Southampton on the opening day of the season, but only played twice more before sustaining the first of a series of injuries.
The latest was a thigh problem which required rehabilitation in the United States.
"He's obviously not ready to play as of yet, but he's working well, so hopefully in the near future he'll be ready," Rodgers told reporters.
"We just want him fit and there's no timeline on that as such."
Johnson, who has missed the last seven matches with a groin injury, is back in full training and could be fit to face Villa.
Lallana injured his calf in the 2-2 draw with Leicester City on New Year's Day.
"He's ahead of schedule in terms of his rehabilitation," Rodgers said. "We're hoping he can join the group tomorrow to train.
"If he's not available for the weekend, then he certainly will be for Chelsea.
"He's a wonderful technician. He's linked up with players when he's played and he will only get better as his time progresses here at the club."
Liverpool face Chelsea in a two-legged Capital One (League) semi-final on Jan. 20 and Jan. 27.
They are unbeaten in their last seven matches since a 3-0 defeat at Manchester United and are eighth in the standings, five points off the Champions League places.
