Irwin, killed in a stingray attack on the Great Barrier Reef on Sept. 4, had a private service at a funeral home in nearby Caloundra, the Brisbane-based Sunday Mail said.
It also said that the local council had given the family permission to bury Irwin, 44, at the 60-acre zoo that has been owned by the Irwin family since 1970.
"Yesterday's service was a service for family and good friends, people who were close to Steve in recent years," the newspaper quoted an unidentified family friend as saying.
"The council gave the family permission to bury Steve at the zoo and we think they're going to erect a monument there so visitors can continue to pay their respects."
Sydney's Sun-Herald newspaper said Irwin's father, Bob, planned to hold a press conference on Monday at the zoo to give details of the funeral.
Calls to John Stainton, Irwin's longtime manager, and Michael Hornby, head of the Irwin charity group Wildlife Warriors, were not immediately returned.
On Saturday, Stainton told CNN's Larry King that the private service would be held soon.
"We are having a private family service in the next two or three days, by Monday" at the latest, Stainton told King. "Then we'll start planning the memorial service which will be open to members of the public."
Stainton also said Irwin's wife, American-born Terri, and his children were coping "quite well" with the death.
"Terri is very, very strong. She's having a lot of sad moments obviously, but she's putting on a brave face for the kids' sake," he said.
The Irwins have two children, Bindi, 8, and Bob, 2.
One venue mentioned for the public memorial service, expected to be held in the next 10 days, is a 52,000-seat sports stadium in Brisbane, the nearby capital of Queensland state.
Irwin could have had a formal state funeral offered by Prime Minister John Howard. Instead, Bob Irwin said his son would have preferred a smaller, private funeral.