The Australian Broadcasting Corporation said Afghan-born Mohammad Ali Baryalei, reportedly a former nightclub bouncer and aspiring actor, was believed to have died in fighting in recent days.
Baryalei has been accused of ordering "demonstration killings" in Australia, including beheading a random member of the public.
"We are currently seeking to verify those reports so I can't confirm at this stage," Bishop said in Canberra.
"It does highlight what the government has been saying, that Australians who leave this country to fight in Iraq and Syria are putting themselves in mortal danger," she said.
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Bishop said the government was urging young Australians not to become radicalised as she defended new foreign fighter legislation designed to prevent citizens from travelling overseas to take part in conflicts.
"We need to ensure that our security and intelligence agencies have all of the powers that they need to ensure that Australians are not taking part in this brutal conflict... But if they do, that they can be arrested and prosecuted and jailed," Bishop told the National Press Club.
The offence carries a maximum penalty of 10 years in prison.
The bill still has to be passed by the lower House of Representatives but is expected to go through easily as it has bipartisan support.
Authorities believe about 60 Australians are fighting alongside militants overseas, including one Sydney man who posed for photos with severed heads.
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.