Community advocate Jamal Daoud says the 22-year-old Melbourne man died during clashes with the Syrian army.
If confirmed, he would be the fourth Australian killed in the war.
But the Department of Foreign Affairs says it hasn't been contacted by members of the man's family or Syrian authorities.
"We stand ready to provide consular assistance to the family, should they request it," a spokesperson said in a statement on Thursday.
Mr Daoud told AAP the Melbourne man's brother announced news of his death on Facebook.
The department reaffirmed its advice that Australians avoid travelling to Syria because of the extremely dangerous security situation.
"The government's capacity to provide consular assistance to Australians in Syria is very limited," the spokesperson said.
Earlier this week, ASIO director general David Irvine warned that the intelligence community was investigating "hundreds" of young Australian men who had joined the civil war in Syria.
Mr Irvine said he was concerned that young Australians were going overseas and "become quite severely radicalised in the extremist Al Qaeda-type doctrines."
