The England international has managed only three appearances for his club this season after picking up a thigh injury on international duty in September.
Having returned to training, Sturridge suffered a setback in November and is currently in Boston continuing his rehabilitation programme.
Sturridge was a key fixture in Liverpool's ultimately unsuccessful Premier League title bid last season and, without him, Rodgers' side have struggled for form this term.
However, after a week in which his side booked a League Cup semi-final berth and gained a dramatic point against Arsenal, the Northern Irishman revealed Sturridge was on course for a January return.
Asked by reporters when Sturridge was likely to be back in action, Rodgers explained: "That will probably be just after the Christmas period.
"The first phase of his rehab was out in LA where we did some specific work with him there.
"He's gone to Boston to pick up the next stage, then he'll move on again to a specialist facility out there and hopefully in the early part of the new year he'll be back and be somewhere close to being fit and playing.
"At some stage in January, we'll look to get Dan back. That will be really exciting for this team.
"We'll put him into the mix again and go back to that flow of our game and results, hopefully."
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