The Anfield club confirmed the Spanish full-back will on the sidelines until February after undergoing surgery on a knee injury that has limited his first-team opportunities this season.
With only on-loan Aly Cissokho and youngster John Flanagan available to replace the 27-year-old, Rodgers is keen to bolster his ranks once the transfer window reopens in the new year.
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"We think Jose will be a few months. It is not a long-term one but will be the new year for sure.
"It is not ideal; you would prefer two in there to really be challenging. Jose is clearly one of the best left-backs in the league and to have him out is a blow."