The 34-year-old Sangakkara is recovering from a broken finger while Kulasekara, 30, has been troubled by a groin strain.
"Kumar is fine," captain Mahela Jayawardene told reporters. "He has been asking our coaches for extra net sessions and is coming along very nicely.
"Nuwan has been bowling at 80 to 90 percent during the last couple of weeks and next week we will let him push himself even further."
Sri Lanka open the tournament with a match against Group C rivals Zimbabwe at Hambantota on Sept 18 and then play South Africa at the same venue four days later.
"We have played at Hambantota before and the wind there presents some challenges," Jayawardene said.
"But it is the same for the other teams as well. With the experience we have we should see how we can use it to our advantage."
The top two in the three-team group will advance to the Super Eight stage.
- Mahela Jayawardene