Jonathan Ansell, 26, who has been in the country for about two years, has not been heard of since he phoned his mother two weeks ago from Melbourne to say he had lost his passport. The man, originally from Glasgow, also claimed he had nowhere to stay and no money.
His was formally reported missing yesterday, after social media appeals failed to result in information.
Mr Ansell, who is described as quietly spoken, may have since travelled elsewhere in the state of Victoria or to another part of Australia.
His mother said: "Jonathan told me that he has been sleeping rough in Melbourne. He has lost his passport and has no money left, his visa also ran out at the end of April.
"I urged him to go to the police or the British embassy, but the call was cut short due to his probable lack of money.
"I felt that Jonathan's self-esteem seemed quite low and he may be having problems communicating effectively due to his circumstances."