Amira Karroum, 22, and Yusuf Ali were widely reported to have been killed in Aleppo on Saturday.
"Consular officials are seeking to confirm the reported deaths of two Australians in Syria," a spokesman for the Department of Foreign Affairs said.
"We strongly advise Australians not to travel to Syria because of the extremely dangerous security situation, highlighted by ongoing military conflict, kidnappings and terrorist attacks."
Australia does not have an embassy or consulate in Syria and Canberra has recommended since April 2011 that its nationals leave the country.
"Sister Amira Ali from the mosque has passed away in Syria with her husband," the devout Muslim, who calls herself "Mujahidah Lioness" on Facebook, wrote on Saturday.
Rose Karroum said the couple were in their house in Syria when the "FSA (Free Syrian Army) attacked and killed them".
Half-brother Karl Karroum said he did not know how Amira, who grew up in Queensland's Gold Coast before moving to Sydney five years ago, came to be in Syria.
"We had no idea she was going to Syria. She left Sydney about December 20, I think, and said she was going to Copenhagen for a holiday with friends and to do some humanitarian work," he told Sydney's Daily Telegraph.
"I mean, her husband lives in Syria, so that's obviously why she went there, but we thought he was going to meet up with her in Copenhagen."
Sheik Omar El Banna, who worshipped with Yusuf Ali at a mosque in the Sydney suburb of Auburn, described him as a good person who had immigrated from the United States to Australia four years ago.
"I hear conflicting reports he was fighting, others say he was doing aid. I believe they were caught in the crossfire," he told the Telegraph.
It is not known how many Australians are in Syria but the conflict has exerted a pull on radicals and last month Australian Federal Police arrested two men in relation to the conflict.
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