Canberra was Tuesday working to verify reports that two of Australia's most wanted Islamic State group fighters, notorious for being pictured holding severed heads, have been killed.

The Australian Broadcasting Corporation cited people close to the families of Khaled Sharrouf and Mohamed Elomar as saying the pair died in fighting in the Iraqi city of Mosul in the past week.

Foreign Minister Julie Bishop confirmed there had been recent drone strikes in the area but said she was still awaiting "absolute verification" they were dead.

"The likelihood of verification in relation to Mr Elomar is probably imminent, however in relation to Mr Sharrouf, we're still seeking to verify the reports," she said.

Sharrouf gained global infamy last year when he posted pictures on his Twitter account showing himself and his seven-year-old, Sydney-raised son holding up the severed heads of slain Syrian soldiers.

Dressed like any other youngster in blue checked trousers, a blue shirt and baseball cap, the picture of the child was captioned "That's my boy", prompting US Secretary of State John Kerry to call it "stomach-churning".

Other photos, thought to have been from Syria, published in Australia at the time showed Sharrouf dressed in camouflage fatigues posing with three young boys, all believed by security agencies to be his sons

Sharrouf, who served almost four years in prison after pleading guilty over a 2005 conspiracy to attack Sydney, fled the country in 2013 along with Elomar.

Elomar, who reacted to the photo of the boy with a tweet to "keep them heads rolling", has also been pictured holding heads of pro-Syrian fighters.

"Both Mr Elomar and Mr Sharrouf rose to international infamy as a result of pictures that they posted of themselves holding up the heads of pro-Syrian fighters. They had been notorious for their violence and their barbarity," said Bishop.

"These two men are not martyrs. They are criminal thugs who have been carrying out brutal terrorist attacks, putting people's lives in danger."

The grandfather of the young boy pictured holding up the severed head told Sydney's Daily Telegraph he was "ecstatic" to hear of Sharrouf's possible death.

"It's a good day isn't it," added Peter Nettleton, whose estranged daughter Tara is married to Sharrouf.

Their reported deaths come as Australia prepares to introduce legislation to parliament this week to strip dual nationals linked to terrorism of their citizenship. It has not been revealed whether Sharrouf or Elomar were dual nationals.

Australia raised its threat level to high last September and has since carried out a series of counter-terrorism raids, with several alleged plots foiled this year.

Canberra has taken a tough stance against radicalised citizens amid alarm at the departure of some 175 of its nationals to fight in Iraq and Syria.

The government this month said about 110 were currently fighting in the two nations, while up to 35 Australians were believed to have been killed and another 30 had returned from the region.