Mr Dunne’s dismembered body was found in the grounds of Castlegreina House on Boreenmanna Rd on December 28. The 64-year-old had been living nearby in Cork Simon accommodation.
Gardaí have confirmed to RTÉ that a team of four detectives from Anglesea Street traveled to Bucharest two weeks ago to locate a 29-year-old man who had been resident in Cork but left the country on December 30.
Local police questioned the man and forensic samples were taken.
The Gardaí utilised the help of Europol in the man's hometown
The man attended a police station to meet with the detectives voluntarily.
It is believed Gardaí may be looking at a possible link between the case and a robbery that took place 24 hours after the body was discovered.
The Echo has contacted the Gardaí for comment.