Australia is considering a possible rescue of the children of an Islamic State of Iraq and the Levant (ISIL) fighter and their Sydney-born mother who have both reportedly died in war-torn Syria.

Tara Nettleton - whose husband Khaled Sharrouf made headlines in 2014 when he posted an image on Twitter of his then seven-year-old son holding the severed head of a Syrian soldier - has died from appendicitis or a kidney condition, Fairfax media reported.

Sharrouf is widely believed to have been killed in a drone strike last year in Iraq, an attack in which fellow Australian Mohamed Elomar also died.

They are in grave danger. We've been in contact with them and there's bombs falling everywhere and people are starving in the streets Charles Waterstreet, lawyer

The family's lawyer Charles Waterstreet told the AFP news agency the couple's five children, aged between five and 14, were trapped in an undisclosed part of Syria.

The 14-year-old daughter gave birth to a child two months ago, fathered by Elomar, and was also looking after her younger siblings, Waterstreet said.

"They are in grave danger. We've been in contact with them and there's bombs falling everywhere and people are starving in the streets," the Sydney-based lawyer said, adding the children have told their grandmother, Karen Nettleton, they "want to get out" of Syria.

"Both their father and their mother are dead and they're victims stuck in a hellhole and they're Australians, and we should be doing everything we can to get them out," said Waterstreet.

Media reports said Karen Nettleton, who campaigned for the Australian government to allow her daughter, grandchildren and great-grandchild to be allowed to return to the country, was only informed of Tara's death in the past two weeks.

It is illegal under Australian law for Australians to provide any kind of support to any armed group in Syria. It is also an offence under Australian law for Australians to enter or remain in the Syrian province of Raqqa - ISIL's self-declared capital.

Peter Dutton, the Australian immigration minister, told journalists outside Parliament House in Canberra on Thursday that he was unable to confirm Nettleton's death, although all Australians were provided with consular assistance regardless of their circumstances.

However, in an interview with a Sydney radio station, he warned the children's experiences since they were taken to Syria by their mother in 2014 to join their father could influence the government's decision on whether they could return home.

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"The conditions under which people are brought back into our country would have to be considered very carefully," Dutton told Sydney radio station 2GB.

"Obviously any parent who is dangerous enough, crazy enough, to take young, impressionable children into that sort of an area obviously scars those children for life," Dutton said.

"So ultimately, the government's clear objective is to keep the Australian public safe and we'd have to look at the individual circumstances to see what the kids may have been through, what they've been exposed to, whether or not later in life they pose a threat."

On Thursday, military analysts told Fairfax Media that attempting a rescue mission into Raqqa to extract the children - should they still be based there - was too dangerous as it was controlled by ISIL.