The left-back, who signed on at Anfield from Valencia last month, picked up an ankle injury during the midweek League Cup tie against Notts County.
It was initially believed that the complaint would not keep him out for too long, but manager Brendan Rodgers has revealed that the Frenchman may now require an operation.
"Aly is on crutches and is looking at four to six weeks out. Whether he just rests it or we decide for him to have a small operation, the timing is around the same," he told reporters.
"It's a blow because he had been training really well. He has slotted in well and would have been a more than adequate understudy for Jose Enrique. Now we need to get him right and get him back playing again."
Rodgers's team face rivals Manchester United later today.