The 25-year-old Asif, who has protested his innocence, was seized at Dubai airport on Sunday while returning home from India after featuring in Indian Premier League.
"Asif appeared before the prosecutor today and recorded a statement in which he said the drug found in his possession was a medicine given to him by a hakim (herbal medicine man) in Pakistan," a Pakistan Cricket Board (PCB) official told AFP.
"Since Friday and Saturday are holidays here in Dubai, so we expect a decision on Sunday," the official, who asked to remain anonymous, said by telephone from the Gulf emirate.
PCB chief operating officer Shafqat Naghmi said the board had received medical reports on Asif ordered by Dubai authorities "but it is not proper for us to disclose their nature."
"Asif has earlier said he had been getting some herbal medicines. I have heard these reports. Sometimes hakims give medicines in which sometimes there are substances which are banned," Naghmi told reporters.
"But this is not the issue. The main issue is to get his release. We respect their (Dubai authorities') procedure. We are confident the truth will come out and there will be justice."
Opening bowler Asif was dropped from the Pakistan squad for next week's tri-series in Bangladesh and replaced by Sohail Khan on Wednesday.
Pakistan captain Shoaib Malik said the team was praying for Asif.
"Our prayers are with Asif, he is a very good bowler, but right now we are concentrating on cricket and the new series which we will see in Bangladesh. I will not comment on this issue because the PCB is handling it," he said.
Asif was banned for one year after he tested positive for the steroid nandrolone in October 2006. Fellow paceman Shoaib Akhtar was banned for two years on the same charge.
The bans were however lifted on appeal two months later. Akhtar meanwhile is appealing a lifetime ban imposed in April for repeated disciplinary problems.