The Federal Government is working to confirm reports that Australia's most infamous terrorists, Khaled Sharrouf and Mohamed Elomar, have been killed while fighting with Islamic State (IS) in Iraq.

A person close to one of the men's families told the ABC's 7.30 program the pair died in fighting in the city of Mosul.

Another source close to the families said they were told Sharrouf and Elomar were killed by a drone strike in the past week.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Listen Duration: 3 minutes 1 second 3 m 1 s Some members of Khaled Sharrouf's family were unaware of reports he may have died overseas. Download 5.5 MB

Elomar's body is believed to have been recovered but the remains of Sharrouf are missing.

Mosul has been declared off limits by the Federal Government, making it hard for security agencies to confirm the information.

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This morning Foreign Minister Julie Bishop said the Government was close to verifying Elomar's death.

"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 this morning.

The image from the Twitter feed of Australian Khaled Sharrouf shows a young boy, reported to be Sharrouf's seven-year-old son, holding the severed head of what is said to be a Syrian government soldier. ( Supplied )

"Given the security situation in Iraq it's difficult for our authorities to gain the kind of information that would be required to verify these reports.

"Mr Elomar was said to be in Mosul. There have been a number of air strikes in Mosul in recent days.

"We are aware that Mr Elomar has been in Mosul for some time."

Sharrouf and Elomar travelled to Syria and then Iraq in 2013, with Sharrouf using his brother's passport to leave Australia.

They shot to global infamy last year when photos were posted online of them holding the severed heads of pro-Syrian government soldiers.

Sharrouf was also wanted by Australian authorities for his role in the suspected shooting execution of an Iraqi official outside Mosul.

Elomar's postings on social media indicated he was a popular and influential figure among Australians who turned up to fight for IS.

If confirmed, their deaths would likely be greeted with relief by security agencies who believed both men continued to reach back to Australia to communicate with young, impressionable Muslims and convince them to travel to Syria and Iraq to fight under the IS banner.

Australian police warrants were issued for both men last year, but they had long professed a desire to die on the battlefields of the Middle East and it was unlikely either would ever return to Australia to be arrested.

Early this year Sharrouf and Elomar were accused of enslaving women from the Yazidi religious minority in northern Iraq.

Deaths would be 'significant blow' to Islamic State

Dr Clarke Jones, a terrorism expert from the Australian National University, said if the reports were true, the deaths of Sharrouf and Elomar would be a "significant blow to Islamic State".

He said they both played a fairly major role, particularly on social media by attracting people to IS.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 2 minutes 33 seconds 2 m 33 s Interview: Dr Clarke Jones ( Emma Alberici )

If the two men were confirmed dead, Dr Jones said it could make people angry and want to go and fight for IS.

"But let's hope it has more of a deterrent value in the sense that it will show young people that even the more experienced fighters and even the core of Islamic State are still in great jeopardy overseas in Syria and Iraq," he told Lateline.

Dr Jones said Sharrouf's wife Tara Nettleton had made inquiries on how she and their children could come back to Australia.

"And I suppose we should have more concern for the kids and trying to get them out of the conflict zone," Dr Jones said.

"I know that one of Khaled Sharrouf's young daughters, [a] 14-year-old, had married Mohamed Elomar, so these two do leave families behind and I suppose in one sense we have some sort of sympathy for the children, but in the atrocities they've committed overseas it's very hard to have any sympathy for them whatsoever."

However, counter-terrorism expert Dr Greg Barton said IS may be relieved if the deaths are confirmed.

Dr Barton said the pair's propaganda value had been exhausted and they were of no military benefit to IS.

"They were stupid, juvenile, not disciplined, not skilled, they had very little to offer," he said.