The Reds skipper, who has played every minute of Liverpool's Premier League campaign this season, has been carrying the injury for some time according to first-team coach Mike Marsh.
"It's looking more and more likely that he might require surgery," Marsh told the club's website.
"He has been playing with a shoulder injury for quite a while now. We'll try to find the right time for him to get it fixed properly.
"It's not ideal timing, it's going to take quite a while for him to heal. It's a funny injury - it's pretty similar to Joe Allen.
"If it needs repairing, it needs repairing and when he's back fit, he's back fit. There's not much we can do about it."