PCB chairman Shaharyar Khan said today that while Ajmal would go for the tests in a few weeks as he was not in the World Cup final squad, Hafeez would take the test by the end of the month.
"Hafeez will take the tests end January so that the results are known before the start of the World Cup. He has already taken an informal test in Chennai and the results were very encouraging and he himself is very confident now he can clear the ICC test and be able to bowl in the World Cup," Khan said.
Hafeez, 34, has been a vital cog in the Pakistan attack, having taken 122 wickets in 153 ODI besides accumulating 4456 runs.
He was suspended from bowling in international cricket in November after he was reported by match officials after the third Test against New Zealand in Sharjah.
The experienced allrounder's bowling action was earlier also reported in the Champions League in India in September.
"Hafeez himself is very confident after the informal test as he said he just needed to do some minor tweeks to his action to clear the ICC test which limits a bowler to 15 degrees to straighten his arm," Khan added.
"Since Saeed is not in the World Cup we are in no hurry to send him for test our priority is Hafeez. But Saeed as informed us he is ready to take the ICC test anytime as he believes he has worked enough on his modified bowling action to clear the ICC requirements," Khan added.
He said Ajmal could also be sent for the test just before the World Cup as he would be required by the national team that has important series against Sri Lanka, England and India in 2015.
Ajmal was suspended from bowling in September by the ICC after failing the official test in Brisbane.