The Department of Foreign Affairs and Trade said it was providing consular assistance to the family.
“We send our deepest condolences to the family at this difficult time,” a spokesperson said.
Speaking to ABC radio, Muslim chaplain Yahya Ibrahim said funeral prayers had been held for the man.
However, DFAT did not confirm the circumstances of the Australian’s death.
One list circulating online suggested at least 550 people died during the five-day Hajj.
A medic who spoke to the Associated Press on condition of anonymity to discuss information not released publicly by the government said that the names listed appeared genuine.
That medic and another official who also spoke on condition of anonymity said they believed at least 600 bodies were at the facility.
However, Saudi officials have not commented on any official death toll.
The Hajj pilgrimage is a religious obligation in Islam, required of every able Muslim once in their life.