Officers in Glasgow were called to a report of a fire in Househill Park near Hartstone Road in Glasgow at around 7.35am on Wednesday, August 4.
Police have said that ‘what appears to be human remains’ were found at the site of the fire.
The death is being treated as unexplained and extensive enquiries are ongoing.
One local woman, who lives close to the park, told The Scotsman she and her neighbours could smell burning and assumed children had been “mucking about”. The serious nature of the incident became clear, she added, when the police arrived.
Supported by specialist forensic teams, officers are still at the scene which is cordoned off.
Police said the area is likely to remain cordoned off for some time.
A Police Scotland spokesperson said: “Additional officers are on patrol in the area and anyone with concerns can speak to them.
"If you have information that would help with our enquiries please call Police Scotland on 101, quoting incident number 0562 of Wednesday, 4 August, 2021.”
A source said: "The remains are very badly burnt.
"It could be days before there are answers about who this person is and what has happened to them."
Stunned residents who live in nearby streets last night told how there was a "burning smell" in the air at around 6.30am – an hour before the find.
One said: "I was leaving for work at about 6.30am and I could smell burning. I didn't see anything, so I didn't think anything of it.
"Later on my neighbour called to say a body had been found on fire in the park. It's terrifying, I can't believe it."
Another said: "It isn't the most quiet place round here but we've never had anything like this. It's shocking, that poor person.
"People will be on edge until we know what went on and someone is caught."
A large section of the park, which is popular with dog walkers and surrounded by homes, currently remains closed.
Fire investigators were also spotted at the scene while police were searching for clues laid out yellow markers nearby.