The striker has not played a Premier League match since August due to a thigh and calf injuries, twice suffering setbacks in a bid to return fo full fitness.
Sturridge, who has one goal in three league appearances this term, subsequently travelled to Boston to continue his rehabilitation.
"Daniel Sturridge is in the final stages of his recovery," Rodgers said. "He will be back in the country in the next 24 hours.
"Daniel is a top-class player, he has wonderful qualities. He will make any team better. I'm hoping he can stay fit and make a charge for us."
"There's no update on Raheem's contract," he added. "That's something between the club and his representatives."
On Milner, he explained: "James is a wonderful player but players get linked with the club consistently."
