Fairfax Media understands the federal government was briefed on Tuesday by intelligence agencies that there was a high level of confidence the jihadist and his sons, Abdullah and Zarqawi, were killed in an air strike in Syria.

It is understood the strike, either by a drone or a manned strike fighter, happened while Sharrouf was driving near the Islamic State defacto capital al-Raqqa on Friday, August 11.

The ABC reported that photos of Sharrouf and his sons' bodies had been circulating among some extremists in Australia.

It is the second time Sharrouf has been reported dead. In June 2015, it was reported that he was killed by a drone strike that also killed his friend and fellow fighter Mohamed Elomar.

It later emerged that Sharrouf was injured but had survived and was in hiding.

National security sources told Fairfax Media on Wednesday that they believe Sharrouf is dead.

The Turnbull government's national security committee of cabinet held a regular meeting on Tuesday and is understood to have been briefed on the situation.

However, family members in Sydney have not gathered to mark the death, as they did in Elomar's case.

Immigration Minister Peter Dutton, speaking in Canberra, said it would be prudent to await further information.

"It's always very difficult to confirm these reports, given that we're dealing with war zones in Syria and Iraq," he said.

"The point to make is that no Australian would mourn the loss of Khaled Sharrouf. He's a terrorist, he sought to harm Australians and, if he returned to our country, he would be a significant threat to the Australian public."

He said the reported death of Sharrouf's children would be regrettable but an inevitable outcome.

"Nobody would want to see Australian children die, nobody would want to see any children die," he said.

"But the fact is Sharrouf and his wife took their children into a war zone, and if they had been killed, what other outcome would they expect? They're obviously horrible people [and] atrocious parents."

Attorney-General George Brandis similarly said of Sharrouf's children that their father had "exposed them to the barbaric practices of Islamic State".

"Australians will well remember the chilling images of Khaled Sharrouf encouraging his own children to hold aloft the severed heads of victims of ISIL. It is incomprehensible that any parent would behave in such a way."

Abdullah, one of the sons understood to have been killed in the recent strike, was shown holding the severed head of a Syrian man in pictures that shocked in the world in 2015.

Senator Brandis said he was aware of reports of the deaths but said "the government's capacity to confirm reports of deaths in either Syria or Iraq is extremely limited".

A media release from the coalition military force's Operation Inherent Resolve said two vehicles were struck in one of 26 air strikes near Raqqa on August 11.

Nineteen tactical units, 35 fighting positions, an IS headquarters and an IS communication line were also destroyed.

Sharrouf, who was released from prison in 2009 after serving time for his role in the Pendennis terrorist plot, left Australia in late 2013 using his brother's passport.

His wife, Tara Nettleton, followed soon after with their five children Zaynab, 15, Hoda, 14, Abdullah, 12, Zarqawi, 9, and Humzeh, 6.

His social media postings - including a photo of Abdullah, then 9, holding a severed head - caused him to become one of Australia's most notorious foreign fighters.

Ms Nettleton died of suspected appendicitis in 2015.

Zaynab has given birth to a daughter fathered by Elomar.

After the 2015 reports of her father's death, she told Fairfax Media: "My father is a shaheed [martyr], just like Abu hafs [Elomar]. Miss them so much."

The government cancelled Sharrouff's citizenship last year, leaving him a citizen of only Lebanon.