Gardaí are still searching the Grand Canal in Tullamore, Co Offaly for any weapons used in relation to Ashling Murphy's murder.
It comes as officers are waiting to question a person of interest in the killing of the 23-year-old school teacher.
Vigils were held around Ireland, and further afield, for Ms Murphy across the weekend.
The man Gardaí want to talk to is understood to still be receiving hospital treatment for a number of injuries, and will need to be assessed before he can be questioned.
Ashling was attacked and murdered while going for a run along the banks of the canal in Tullamore last Wednesday.
Conor Lally is crime and security editor with the Irish Times.
He told Newstalk Breakfast medical staff alerted the Gardaí last Thursday.
"The chief suspect is obviously still in hospital being treated for those injuries.
"While he is there, Gardaí are essentially waiting to be able to speak to him - he has to be assessed - some of the wounds that he had were quite serious.
"We just don't know when he'll be interviewed by the Guards.
"We know that he has links to the Co Offaly area, he's a man who has a partner and children.
"He presented to hospital in the company of a relative of his last Thursday evening.
"He really had wounds that he wasn't able to explain - and when medical staff started talking to him, they very quickly established that he had links to the Tullamore area.
"Because of that, and because he had wounds that he wasn't able to explain, they called in the Guards.
"And really when the Guards started doing their checks on him, he very quickly became a person of interest".
Weekend searches
But Conor says the investigation is progressing separately.
"There was an awful lot of work that went on during the weekend: people will have seen that there are searches now really all over the place.
"There's been two vehicles taken in by the Guards, they're being examined.
"There's been a house in Co Offaly which has been searched... and there's been a house in south Dublin that's also been searched since the end of last week."
And he says work on the canal is still ongoing.
"While all of that's been going on, the Grand Canal is still actually being searched by Garda divers - and specifically what they're looking for there is any weapon that the killer may have had on him.
"That work is actually still underway".
Gardaí are asking anyone with information to contact Tullamore Garda station on 057-932-7600, the Garda Confidential Line at 1800-666-111 or any Garda station.
