The Irish Independent states that the man in the same house as a woman who was discovered in a wardrobe, has talked to the Gardaí.
The suspect is currently in hospital after jumping from a third floor window when Gardaí arrived at the premises on Thursday evening.
The man in question was well known to Joanne Lee and sustained serious leg injuries from the jump.
He is understood to have told investigating officers last night that he "had to kill" Ms Lee.
A Garda media briefing surrounding the death of the missing woman also confirmed that the woman was found wrapped up tightly in a sleeping bag and bedsheets.
The 38-year-old's body was discovered in the wardrobe at a property on Ranelagh Road after Gardaí were called to the scene as part of an investigation into a missing persons case.
Anyone who may have any information is asked to contact Donnybrook Garda station on 01 666 9200, the Garda Confidential Line on 1800 666 111 or any Garda station.