The 32-year-old, who has featured in every minute of the Reds' 34 Premier League matches so far, has been playing through the problem this season.
"It's looking more and more likely that he might require surgery," Marsh told Liverpoolfc.com. "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."
He added: "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 (who has already had surgery which has ruled him out for the remainder of the campaign).
"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."
If, as expected, he undergoes an operation, Gerrard is likely to miss internationals against the Republic of Ireland at Wembley on May 29 and Brazil in Rio de Janeiro on June 2.
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