The Attorney General (AG) of the emirate, where the 25-year-old paceman was detained June 1 as he was returning home from India after featuring in a cricket event, will conduct the inquiry.
"Our lawyer has confirmed that Asif's case will start on June 22 and no charges have yet been lodged against him," said Pakistan Cricket Board (PCB) chief operating officer Shafqat Naghmi.
Asif has appeared before Dubai prosecutor, Mohammad Ali Rustan, who was quoted in Gulf media as saying opium was found in the cricketer's possession.
PCB chairman Nasim Ashraf last week said his board will initiate its own inquiry once Asif returns home.
"We have maintained that Asif is innocent until proven guilty and all speculations on the case are unwarranted," Naghmi said.
Asif was banned for one year after testing positive for the steroid nandrolone in October 2006. Fellow paceman Shoaib Akhtar was banned for two years on the same charge.
The bans were lifted on appeal two months later.
Akhtar is appealing a lifetime ban imposed on him in April for repeated disciplinary problems. His case resumes Saturday.