Mr Hourihane, a former chef from Bantry, died in the early hours of October 13 last following a brutal assault in the Mardyke Walk area of the city. He and other homeless people had gathered to live in tents.
He was found close to his burning tent, with severe injuries. He was rushed to Cork University Hospital but died shortly afterwards.
Chief Superintendent Barry McPolin said: “We are at an advanced stage. I am unable to comment for operational reasons but a huge amount of work has gone into the case.”
Nobody has been arrested and the Garda investigation is continuing into the attack on Mr Hourihane, who was well known in Cork city.
Anyone with information on the killing has been asked to contact Anglesea Street Garda Station on 021 4522000, the Garda Confidential Line on 1800 666 111 or any garda station.