Police are keeping an open mind on who the person is but so far the strongest lead is the former owner of the house.
The property was owned by David Stanley Hart until recently.
Neighbours told the Herald Hart was a "recluse" who went abruptly missing at least a decade ago.
Murray Goldings, 45, has lived in Marlborough St his whole life and said Hart had lived at the property ever since he could remember and used to run a boarding house out of it for older residents.
A source said there were "heaps" of people moving in and out of the boarding house and the body could be one of a number of people.
But Hart seems the most likely lead to start with.
The scene examination is ongoing and is expected to take several more days.
Police are appealing for anyone who lived at the property, which operated as a boarding house for some years, to come forward.
In a statement this afternoon Acting Detective Inspector Glenn Baldwin said staff transported the body to the mortuary last night.
They also removed a large piece of concrete from the scene, which ESR scientists will continue to examine over the ensuing days.
He said the post mortem was "meticulous and challenging work" for the pathologist and his findings were not expected to be available to police for some time.
"The identity of the deceased remains unknown," Baldwin said.
"There are considerable challenges for police, who remain open minded on this point.
"It is possible that the deceased died some years ago.
"Given the circumstances, formal identification will require forensic evidence."
Baldwin said obtaining a DNA profile from the body "may take a week or two".
"But identification can only occur if police and ESR have a comparative DNA sample, that the deceased's DNA can be compared to," he explained.
"Therefore it could likely be several weeks before the identity of the deceased is known.
"Until such time, police will not be speculating on the deceased's identity.
"The focus of the investigation continues to be on establishing the identity of the deceased, which includes identifying and speaking with former occupants and residents."
Baldwin would not be drawn on Hart including whether police were looking for his family.
"This is a challenging and complex investigation which is expected to take some time before we are in a position to establish the circumstances surrounding the death," he said in the statement.
"We have had a really positive response from people contacting us with information on 105, which has been really helpful.
"That said, we continue to seek assistance from the public to identify and locate former occupants, owners and residents at the premises, which we understand was possibly a former boarding house."
In 2017, 3 Marlborough St was sold to a new owner.
Other residents in the street also remembered Hart but told the Herald they hadn't seen him in years.
"We kind of knew him. He was a bit of a recluse. Haven't seen him in a long time," Goldings said.
"He used to always have a little garage at the front that got knocked down. He was always in there tinkering away. He was in his 70s."
Before the 2017 sale, the house had continued on as a boarding house of sorts - but neighbours just stopped seeing Hart there.
"Yeah there was all kinds of people coming and going," Goldings said.
Goldings and another resident on the street said they understood the bank eventually took the house and resold it after being unable to get in contact with Hart.
"That's what we heard [the bank took the house]. Because it came up for a mortgagee sale," Goldings said.
"Our guess was that he'd gone missing and he had money in the bank and they had taken money out until the money dried up and they couldn't find him.
"There were rumours he went to Australia and there was another rumour he had dementia and had gone to a home somewhere. I reckon it would be over 10 years ago.
"He disappeared, no one knew [why] and there were all these rumours."
In November 2018 the Grey District Council sought Hart in relation to a property he owned in Blackball.
A notice in the local paper stated that unless Hart claimed the land at 24 Stafford St and paid all outstanding rates within a month, the council would apply for a court order declaring it to be abandoned and to authorise the sale or lease.
The notice stated Hart's whereabouts were "unknown".
Property records show 24 Stafford St is still owned by Hart.
The Herald has sought comment from the local council.