Speculation is brewing that Sydney terrorist Khaled Sharrouf faked his own death in a bid to orchestrate his family’s return to Australia.

Security officials have reportedly begun to investigate the possibility, after Sharrouf was rumoured to have been killed along with fellow Islamic State (ISIL) fighter Mohamed Elomar in a drone strike in early June.

“That is certainly a possibility,” a senior intelligence source told The Daily Telegraph on Sunday night.

• More doubts over Sharrouf’s demise
• Sharrouf ‘the target’ of strike
• ISIL recruits Sharrouf, Elomar dead: reports

The family of Sharrouf are reportedly trying to come home.

The source said they were not sure if Sharrouf was alive or dead. “The fact is we don’t know yet,” they said.

Sharrouf’s mother-in-law, Karen Nettleton, previously called on Prime Minister Tony Abbott to allow daughter Tara Nettleton and her five children to return to Australia.

Fairfax Media published a text message purported to be from Sharrouf’s eldest daughter Zaynab – who is said to have married Elomar at the age of just 13 – to her grandmother Karen Nettleton in Sydney.

“My husband got hit by a drone yesterday and got killed,” she wrote on June 20.

Karen Nettleton said last week that she was told of Elomar’s death when a messenger visited her at home.

“I was also told that Khaled Sharrouf, my daughter’s husband, was missing and presumed dead,” she said.

In an interview to be aired on ABC’s 7.30 program Monday night, Ms Nettleton said the Australian Federal Police (AFP) was initially willing to help when contacted about a year ago, but had gone cold on the idea.

“I was devastated, because, who else do you go to get help to get your children out of a place like that? I certainly can’t go there and get them,” she said.

Opposition Leader Bill Shorten said security agencies, not politicians, should be left to deal with the Sharrouf family.

“We don’t need politicians second-guessing our defence and security experts,” Mr Shorten told reporters in Melbourne on Monday.

He again queried why the parents had taken their children to the middle of a “hell hole” in the first place.

Last week, Immigration Minister Peter Dutton said the Sharrouf family should make contact with the AFP.

While authorities now appeared certain Elomar was killed in a drone strike earlier this month, there was less confidence about the fate of Sharrouf who was initially believed to have also been killed in al-Raqqa, the ISIL’s self-proclaimed capital in Syria.

Highly classified images captured by the US military had reportedly confirmed Elomar was killed.

Foreign Minister Julie Bishop on Sunday said authorities were attempting to confirm the latest reports about whether Sharrouf was dead for alive.

“Our security and intelligence agencies are working to verify reports that Khaled Sharrouf survived a coalition air strike which is believed to have killed Mohamed Elomar,” Ms Bishop said.

Elomar and Sharrouf, who travelled to Syria in 2013, gained notoriety last year when they posed for photos holding the severed heads of enemy fighters.

– with AAP