The claims have raised the potential for his young family to be repatriated from the Middle East, Australia's foreign minister Julie Bishop said.
She said the authorities were attempting to verify the recent deaths of Australians Khaled Sharrouf and Mohamed Elomar in the Islamic State-held city of Mosul in Iraq.
Both men were seen in photographs posted on social media holding heads of Syrians.
Fairfax Media newspapers reported last month that the Australian family of Sharrouf's Muslim-convert wife, Tara Nettleton, was trying to help her bring her three young boys and two teenage daughters from Syria home to Sydney.
Sharrouf's seven-year-old son horrified the world a year ago when he was photographed holding the severed head of a Syrian soldier by the hair.
US secretary of state John Kerry described it as "one of the most disturbing, stomach-turning, grotesque photographs ever displayed".
Ms Bishop said that Sharrouf's death would have to be verified before Australia considers repatriating the family.
"We understand that there are family members in Syria or Iraq and should these reports be verified, then we will try to be in contact with them," she told Australian Broadcasting Corporation.
But the government will not guarantee that the family can return.
"It would depend very much on the circumstances and the advice that we receive from our intelligence agencies at the time," Ms Bishop said.
Sydney-born Sharrouf, who was also a Lebanese national, was a prime target of legislation to be introduced to Parliament this week that would allow terrorists who are dual nationals to be stripped of their Australian citizenship.
The government estimates that up to half the Australians who have travelled to Iraq and Syria to fight for Islamic State are dual citizens.
The government has also passed contentious new laws that make it a criminal offence to even visit Mosul or the IS stronghold of al-Raqqa province in Syria, where the Sharrouf family was thought to be based.
Sharrouf was among nine Muslim men accused in 2007 of stockpiling bomb-making materials and plotting terrorist attacks in Sydney and Melbourne, Australia's largest cities. He pleaded guilty to terrorism offences in 2009 and served less than four years in prison.
Sharrouf slipped out of Australia in late 2013 using his brother's passport because his own had been cancelled. Ms Nettleton later took their children to Syria to reunite with her husband.