The 32-year-old Gerrard has played every minute of every match in the English Premier League this season. The team has four matches remaining.
Liverpool assistant coach Mike Marsh says Gerrard "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."
If Gerrard has surgery right after the season ends on May 19, he would likely miss two matches for England, including a friendly against Brazil on June 2 at Maracana Stadium.