The Anfield club confirmed the Spanish fullback 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.
"It is certainly something that – if Jose is going to be out for a long time – we would have to look at for sure," he said. "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."