The Spanish left back came off the bench in the 4-0 Premier League thrashing of Fulham before the international break after being sidelined since the victory over Crystal Palace in October.
However, Enrique has suffered a setback and Rodgers has expressed his frustration at losing the former Newcastle man once again.
"Jose Enrique has been struggling for a little while with an injury," he told talkSPORT. "He will probably need an operation. It’s a blow for us because he's a very talented player."
Liverpool returns to Premier League action with a mouth-watering Merseyside derby clash against Everton at Goodison Park on Saturday.