The goalkeeper missed the 3-2 victory over Tottenham last Sunday with a calf problem but coach Mike Marsh is optimistic about his chances ahead of the game at St Mary's.
"He's coming along nicely. He's got one of those injuries where you're not sure how long it's going to take," Marsh told Liverpool's official website.
"He's still getting treatment - with a bit of luck that will improve in the next couple of days and he'll be available for Saturday."
Marsh also confirmed midfielder Joe Allen requires surgery on a shoulder problem - but was unable to confirm when that might take place.
He added: "I think he will need surgery. We'll try to get that out of the way sooner rather than later so he'll be ready for pre-season.
"We'll just see how the rest of the squad is before we commit to that."
Allen, who came on as a second-half substitute against Spurs, has been named in the Wales squad for the upcoming World Cup qualifiers against Scotland and Croatia.