Detective Senior Sergeant Chris Adams said police have been inundated with information from the public and now want to speak to a blonde Caucasian woman in her mid-20s who was spotted near Ms Vulin's riverside Rivervale apartment around the time of the attack.

Senior Sergeant Adams also said the crime scene indicated that she knew the person who doused the 25-year-old in fuel and set her alight a week ago.

Police are now urging the woman, who was seen between 5.45am and 6.45am last Thursday, to come forward to help detectives with their enquiries.

Ms Vulin's sister, Svetlana Velickovski spoke to the media for the first time today following the deliberate attack.

"This is clearly a maniac," Ms Velickovski said.

"Our family are living minute to minute, we can't eat, we can't sleep, if you know what happened you have to come forward and let police finish this.

"Dana is extremely critical and every minute she is alive is a miracle," a visibly upset Ms Velickovski added.

Ms Vulin, who suffered burns of up to 60 per cent of her body, underwent the first in a long line of skin graft surgeries on Tuesday evening.

"Dana is stable but critical... we hope to rest ourselves for the first time in a while," her family posted on the We Heart Dana Vulin Facebook page late Wednesday evening.

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