The 37-year-old, ranked number one in one-day internationals and Pakistan's main bowling weapon, had his action reported as suspect during the first Test against Sri Lanka at Galle earlier this month.
Under International Cricket Council (ICC) rules Ajmal is required to clear his action from an accredited biomechanics lab within 21 days of the report, but he is free to play until then.
Pakistan Cricket Board (PCB) chief operating officer Subhan Ahmed said Ajmal will have tests in Brisbane.
"Ajmal will be sent to Brisbane to undergo tests and a PCB official will go with him," Ahmed told AFP. "The team management is arranging for his travel from Sri Lanka."
Team manager Moin Khan said Ajmal is in Hambantota where Pakistan will play the first of three one-day internationals on Saturday.
"If he gets a flight on Friday then he will miss the first one-day (match) but we are trying to get him back by August 26 in time for the next game a day later in Colombo," Khan told AFP.
The third and final match is in Dambulla on August 30.
Ajmal's action was first reported in 2009 but he was cleared as there were only doubts over his "doosra," a special delivery which turns the other way than a normal off-spin.
However, this time match officials have raised concerns over several deliveries including some bowled from over the wicket, raising threats he could face a ban and would need remedial work on his action.
Sri Lanka's Sachitra Senanayake and New Zealand's Kane Williamson - both off-spinners - were also reported and subsequently banned from bowling after their actions were reported last month.
Senanayake has undergone remedial work in Western Australian University last week but will have to wait a report from the University to get clearance.
The Pakistan team will be hit hard if Ajmal is banned as they face tough series against Australia and New Zealand in the United Arab Emirates from October to December.
He is also a crucial part of Pakistan's lineup for the World Cup in February-March next year.
Ajmal has so far taken 178 Tests 182 one-day wickets. He is the leading wicket-taker in Twenty20 internationals with 85.
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