If the 32-year-old, who has been ever present in this season's league campaign, has surgery in the close season he could miss England's friendlies against Ireland at Wembley on May 29 and away to Brazil on June 2.
"It's looking more and more likely that he might require surgery," first team coach Mike 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... 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."
The midfielder, who is due to have a testimonial match against Greek champions Olympiakos at Anfield on August 3, has scored nine league goals this season.
He has made 628 appearances for the Merseyside club where he has spent his entire career after coming through the youth ranks, scoring 159 goals.
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