A man who was spotted wandering around on the street on Friday morning is believed to have had a mother-of-three.
Valerie French Kilroy was found dead in Westport, Co Mayo, at around 10am on Friday.
A source reportedly said police had been alerted to the man wandering near the victim's house naked and in a distressed state.
It is said that they proceeded to arrest him, and he claimed responsibility for the mother's death, the Irish Mirror reports.
Police then reportedly rushed to the home as soon as they were there, and found them all unharmed.
A source said: "Gardai in the area was alerted to this man walking around in distressed state.
"He was arrested and taken to the Garda station where he claimed he had killed Valerie.
"Teams of officers are dispatched to the house immediately."
The source added that while a post-mortem examination will take place Saturday, police believe they are dealing with a murder case.
The man was arrested in the Castlebar Garda Station, the source added.
It's believed Valerie's three children, a boy, five, and younger twins, were in her bungalow at the time of her death.
Her body remained at the scene on Friday evening underwent a forensic examination.
A spokeswoman confirmed that investigators are not looking for anyone else in relation to the incident.
She added: "The family of the deceased has been appointed and has been appointed.
"The Garda investigation is ongoing.
"An incident has been established at Castlebar Garda Station.
"Gardaí are appealing for witnesses or anyone who can assist with this inquiry to contact Castlebar Garda station on 094 9038200 or the Garda confidential line on 1800 666111."