The woman, reportedly an Israeli student in her 20s, was found dead just metres from a Melbourne tram stop on Wednesday morning.
According to media reports, the Israeli consulate in Australia is arranging for her body to be returned to her family.
Police are expected to further canvass nearby streets on Thursday in a bid to determine how she died and what led to her body being left at the stop near a shopping centre at Bundoora in Melbourne's north.
They have confirmed they are treating the death as suspicious.
The woman's body was found in scrub near a Bundoora shopping centre on Wednesday morning by passers-by and a Homicide detective later said it was likely the woman had travelled on the route 86 tram from Docklands overnight.
Detectives are now investigating if the woman was sexually assaulted and are scouring CCTV footage from the tram.
Police have not formally identified the woman. SBS News has contacted the Israeli consulate.
Police believe the woman was assaulted before she was murdered in Bundoora, Melbourne. Source: AAP
"We are treating it as suspicious. It's apparent or it seems that the female has been assaulted," Inspector Andrew Stamper told reporters near the scene on Wednesday.
"We would ask for anyone that may have dashcam footage, CCTV or may have seen anything here that could be a small piece in the jigsaw puzzle to contact Crimestoppers."
