Recent reports had claimed that the England international would need to go under the knife to mend the problem that is believed to have troubled him for some time.
Speaking to the club's official website this afternoon, Marsh confirmed the speculation but said that no date for an operation has been set.
"It's looking more and more likely that he might require surgery," said Marsh. "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."
Gerrard has featured in all of Liverpool's Premier League matches this season.