But Save the Children have raised concerns about the boy's safety and wellbeing after speaking with his family.
At least 200 prison inmates and militants and 30 security forces have been killed since Islamic State militants attacked the jail last week in a bid to free their members held there, officials have said.
The Kurdish-led SDF, with US air support, this week regained control of the prison in the northeastern Syrian city of Hasaka.
The boy is in the custody of the US-backed Syrian Democratic Forces (SDF) and coalition forces.
Save the Children has called on the Australian government to step in and act before an Australian child dies, saying he hasn't yet received any medical assistance.
In the recorded messages from when he was in the Guweiran prison, the boy said he was bleeding from bullet wounds.
"I just got shot by Apache (helicopter), my head is bleeding, I have injured my head and my hand," he says.
"I need help, we're getting hit from every side from the Kurds, we're getting hit by planes."
Middle Eastern media organisation Al Jazeera reported SDF commandos closed in on the Syrian prison on Wednesday and captured Islamic State fighters.
At least 550 suspected IS fighters surrendered to the US-backed forces as they wrestled back control of the prison, the outlet reported.
The home affairs department said the Australian government does not comment on the circumstances of individuals.
with Reuters
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