The autopsy on Monis, who was killed when his 16-hour siege of a Sydney cafe came to a violent end on Tuesday morning, began on Thursday and could be completed as early as Friday.
The bodies of his two victims, Katrina Dawson, 38, and Tori Johnson, 34, were released to their families on Thursday night.
The NSW Justice Department, in a statement issued on Friday, said once the autopsy was completed, a burial order would be made releasing the body to the next of kin.
However, it's possible taxpayers may have to pay for the funeral.
Monis, who was on welfare at the time of the siege, may not have had assets to pay for the arrangements.
It is unclear whether his de facto partner Amirah Droudis, who is out on bail on charges over the murder of Monis' ex-wife, will claim his body.
Droudis, 34, has been charged with the murder of 30-year-old Noleen Hayson Pal, who was stabbed multiple times and set alight in a western Sydney unit block.
"If no one comes forward to claim his body, a destitute burial will be organised through NSW Health," the Justice Department said.
Under rules governing cases that involve the coroner, and where no next of kin can be found willing to make funeral arrangements, the Department of Forensic Medicine can arrange a destitute funeral.
The Public Health Unit then requests a burial or cremation from the contracted funeral director who forwards the invoice to the Public Health Unit for payment.
According to Sharia law Monis, who was Muslim, would have to buried.
If no-one claims the body, and the deceased is to be buried, it will be in an unmarked grave.
The 50-year-old was killed when the siege ended in a volley of bullets after 2am on Tuesday.
