The woman, 23, might have jumped in to try and save her drowning boyfriend, Victoria Police said, adding they remain in the intensive care unit of a local hospital.
The couple, who moved to Australia two years ago and live together in Preston area, were at the WaterMarc aquatic centre at Greensborough in northeast Melbourne when they were found unconscious in the pool, police were quoted as saying by 'The Age' newspaper.
Paramedics said the man was not breathing and had to be revived.
Senior Sergeant Justin Goldsmith said there was a small mark on the on the man's forehead but the couple had no other obvious wounds.
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"There's no indication as to what sort of incident took place for this to happen," said Goldsmith. "There's a small abrasion on the man's forehead, it's a possibility there's been a head clash but there may be other avenues we are investigating."
"Whether she was wearing clothes for cultural reasons, was just standing on the side and not intending to get in the water, or whether she jumped in to save the other man is pure speculation. We just don't know, which is why we're really desperate for witnesses to come forward."
Goldsmith said there was a "strong possibility" that one or both of the victims were already in the water but got into trouble. Both were inexperienced swimmers, he added.
Family of the couple are travelling from India and other parts of Australia to be with them, the report said.