The woman, 37, and two girls aged eight and 10 were injured when a gas cylinder exploded inside their home in Melbourne's east on Wednesday night.
The girls are in a stable condition at the Royal Children's Hospital while their mother remains fighting for life in the Alfred Hospital.
A Victoria Police spokesperson said the woman is not in a position to speak with detectives, who are keen to discuss the fire with her.
A 36-year-old man who lives at the townhouse, but not there at the time, has spoken to police and been ruled out as a suspect.
Dozens of firefighters battled the raging blaze at the Chadstone home, with flames seen burning through the roof of the two-story townhouse.
Fire crews found the woman and two girls unconscious in an upstairs bedroom and carried them from the smoke-filled home, which Fire Rescue Victoria Commander Paul Eckholdt described as a "difficult rescue".
"They were carried out and taken out to the front where Ambulance Victoria paramedics and firefighters were waiting," Cmdr Eckholdt told ABC Radio.
"They did have some burns, and they also had some airway burns as well."
The fire destroyed bedrooms, an ensuite and caused a partial structure collapse while the rest of the home received smoke and water damage.
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