According to RTE news he has been identified as 64-year-old Frankie Dunne.
They report that his body was found decapitated and without arms.
A murder investigation is under way into his death.
Mr Dunne had been living south of the River Lee on Boreenamanna Road in recent months at high-support housing operated by Cork Simon, which is a few minutes' walk from where his body was discovered.
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Detective Superintendent Michael Comyns said Mr Dunne's body was discovered by a neighbour in the backyard of Castlegreina House, a two-storey detached house at the city end of Boreenamanna Road, and gardaí believe his body was only at the scene for a few days.
Det Supt Comyns could not say if the murder took place in the area where the body was found and added that gardaí were conducting house-to-house inquiries as part of their investigation.
Castlegreina House has been unoccupied for years and there have been incidents of anti-social behaviour in the area as people gathered there to drink.
Anyone with information is asked to contact Bridewell Garda Station on 021 4943330, the Garda Confidential Line on 1800 666 111, or any garda station.