The man, who was not named, was believed to be from south-west Sydney and married with children, according to the Sun Herald.
Australia's Department of Foreign Affairs said it was attempting to verify the reports, but it was "very difficult to do so".
"Due to the extremely dangerous security situation consular assistance is no longer available within Syria or Iraq," a foreign ministry spokesman said in a statement.
The reports came two weeks after Afghan-born Mohammad Ali Baryalei, Australia's most senior IS recruit, was reportedly killed in Syria.
The Herald reported that another IS fighter from Sydney, Abu Noor al-Kurdi, was also killed with Baryalei.
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It followed claims that hardline IS chief Abu Bakr al-Baghdadi was killed in US-led airstrikes near the Iraqi city of Mosul on Saturday, although US officials could not confirm if he had been present.
The Australian government passed a law criminalising travel to terror hotspots in October, in response to fears about the flow of foreign fighters to the Middle East.
Some 70 Australians are believed to have already made the journey, with another 100 supporting them with recruitment and funding from home, the government has said.
An estimated 20 jihadists who fought with terrorist groups in the region have also returned to Australia, while a further 73 people have had their passports cancelled to prevent them joining the Islamic State group, Canberra said.
Fifteen Australians, including two suicide bombers, are already thought to have died fighting in Syria and Iraq, Australia's then intelligence chief David Irvine said in late August.
The country raised its terror threat level in September and carried out extensive counter-terrorism raids in Sydney and Brisbane, with Attorney-General George Brandis warning last week that Australians should brace for more large-scale operations.