An investigation was launched after emergency services were called to the incident in the Pollok area of the city.
Officers received reports of a fire in Househill Park in Glasgow on Wednesday morning, and later confirmed that human remains were found at the scene.
It is understood that Police Scotland are carrying out door-to-door inquiries in Pollok after announcing that the death is being treated as unexplained.
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”.
Residents who live nearby 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, was closed off.
Fire investigators were also spotted at the scene while police were searching for clues laid out yellow markers nearby.
Forensic teams were also spotted in the park after the discovery.
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."
A Police Scotland spokesperson said: “Around 7.35am on Wednesday, 4 August, officers were called to a report of a fire in Househill Park near Hartstone Road in Glasgow.
“What appears to be human remains were found at the site of the fire. This death is being treated as unexplained and extensive enquiries are ongoing.
“Officers, supported by specialist forensic teams, are still at the scene which is cordoned off and is likely to remain so for some time.
“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."