Sangakkara was ruled out of action in July due to a fractured finger. However, he was named in Sri Lanka's squad for World T20 subject to proving his fitness.
"Kumar is fine. He has been asking our coaches for extra net sessions and is coming along very nicely," said Jayawardene in Colombo on Monday.
Another player who has been recovering from injury is Nuwan Kulasekara. Jayawardene said that the bowler was "bowling at 80 to 90 percent".
"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," the Sri Lankan skipper added.
Hosts Sri Lanka, who are in Group C, will face Zimbabwe in Hambantota on September 18.