Herath, 36, split the webbing between two fingers on his bowling hand trying to take a return chance off Jos Buttler in a thumping defeat of England on March 1.
The left-armer missed the last two pool matches against Australia and Scotland but the stitches have been removed from the wound and he will be given until training on Tuesday to prove his fitness.
"Rangana is recovering fast and I hope he will be alright," Jayasuriya told reporters beside the nets at the SCG.
"The stitches have been taken off and he'll be ready for the match. That's what I'm thinking, it will depend on today and tomorrow, probably tomorrow."
The Sri Lankans have been bedevilled by injury problems at this World Cup but all-rounder Angelo Matthews has recovered from an Achilles issue and will lead the side on Wednesday.
Leg-spinning all-rounder Seekkuge Prasanna was brought into the squad, effectively as a stand-in for Rangana, and took 1-77 in the loss to Australia last week at the SCG, a ground which has a tradition of providing some turn for spinners.
Rangana has taken three wickets at a cost of 49 runs in his previous two ODI matches at the SCG but Jayasuriya said spin bowling would not necessarily be crucial to Sri Lanka's chances of reaching the semi-finals for the fourth straight World Cup.
"We have fast bowlers, we have spinners, we don't have any concrete plans, we'll just stick to the basics," he said.

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