The tourists have other concerns ahead of the November 8 Test, with senior opening batsman Sanath Jayasuriya recovering from a virus and veteran seamer Chaminda Vaas nursing a foot complaint.
Spin wizard Muttiah Muralitharan will be rested from the three-day tour game against Queensland starting on Friday as he recovers from a bicep injury.
Sri Lanka coach Trevor Bayliss said he has no problem with resting Muralitharan after his marathon stint of 4-122 against a Cricket Australia Chairman's XI in Adelaide this week.
"He bowled 44 overs at Adelaide in his first competitive bowl for a few months after injury," he said.
"We did not want to overdo it with him. Someone with his experience, he doesn't have to bowl a terrible lot to put the ball on the spot." Wicketkeeper-batsman Sangakkara suffered his hamstring injury during the draw at Adelaide.
"Kumar's still struggling a little bit. He definitely won't be playing in the match against Queensland," Bayliss said.
"He's under a cloud for the first Test. We will just have to see what he is like in a few days' time.