Detectives investigating the violent death of a woman whose body was found naked and battered in Melbourne's Kings Domain precinct, next to the Royal Botanic Gardens, are searching for a homeless man who is believed to have been sleeping in a nearby rotunda.

The woman, aged in her 30s, is believed to be from China and was in Australia working in the hospitality industry.

Homicide squad detectives are investigating whether she was sexually assaulted and killed while walking to work, Detective Sergeant Nathan Favre said.

"We can't rule out sexual assault as the motivation for this offence,” he said. “Certainly the manner in which the deceased was located, in a state of undress, indicates that may have been the case."

Police believe they know who the woman is, but have not been able to contact her family.