Herath, 36, part the webbing between two fingers on his bowling hand attempting to take a return risk off Jos Buttler in a pounding thrashing of England on March 1.
The left-armer missed the last two pool matches against Australia and Scotland yet the fastens have been expelled from the injury and he will be given until preparing on Tuesday to demonstrate his wellness.
"Rangana is recouping quick and I trust he will be okay," Jayasuriya told journalists close to the nets at the SCG.
"The join have been taken off and he'll be prepared for the match. That is what I'm considering, it will rely on upon today and tomorrow, most likely tomorrow."
The Sri Lankans have been bothered by harm issues at this World Cup yet all-rounder Angelo Matthews has recuperated from an Achilles issue and will lead the side on Wednesday.
Leg-turning all-rounder Seekkuge Prasanna was brought into the squad, adequately as a stand-in for Rangana, and took 1-77 in the misfortune to Australia a week ago at the SCG, a ground which has a custom of giving some turn to spinners.
Rangana has taken three wickets at an expense of 49 runs in his past two ODI matches at the SCG however Jayasuriya said twist playing would not so much be essential to Sri Lanka's possibilities of coming to the semi-finals for the fourth straight World Cup.
"We have quick bowlers, we have spinners, we don't have any solid arrangements, we'll simply stick to the essentials," he said.
