The suspect remained in a Dublin hospital last night where he was still being treated for a number of injuries which are believed to have been self-inflicted.
“The investigation is going very well at the moment,” a senior source told the
"Huge progress has been made over the past 72 hours.”
Specialist gardaí were making preparations yesterday to interview the suspect and there is an expectation that this may happen today as soon as he is discharged from the hospital.
Senior sources have also revealed that officers have spoken to a number of family members and close associates of the suspect in the “hope of building up a full picture of this individual”.
Gardaí will only seek to speak to him when he is deemed medically fit to be questioned.
Ashling (23) was killed in a crime that is still being classified as “random” as she was out for a run on the banks of the Grand Canal in Tullamore at around 4pm last Wednesday, having finished work just an hour before at Durrow National School.
The Garda Sub-Aqua Unit continued to search the canal yesterday while there were also major searches at a property outside Tullamore and at a house in Crumlin as well as another home in Dublin.
All of these have links to the hospitalised suspect. A dig began on Saturday in the back garden of the Co Offaly house.
It is understood the suspect was brought to hospital from the property in Crumlin on Thursday evening by a person known to him.
He has been in hospital since then. Officers were alerted to his presence there because medics became suspicious of his injuries.
He is believed to have left Tullamore after the murder and travelled to Dublin where it is suspected he inflicted injuries on himself.
A car has been seized as part of the investigation and sources say that “excellent quality” CCTV has also been obtained.
“There is nothing in this individual’s background to suggest that he would be capable of such an horrific crime,” a senior source said last night.
The suspect is a father who has lived in Offaly for a number of years.
Gardaí have also been carrying out detailed forensic examinations as part of the investigation but there has been “no breakthrough yet” in terms of this part of the probe, a senior source said.
A number of DNA samples have been obtained but these profiles have not yet been identified.
Gardaí have stressed that the nomination of possible suspects during an investigation is routine and urged the public against attributing blame to individuals or sharing their identities during an ongoing investigation.
Sources say that forensic evidence is expected to play a big part in the investigation as the Falcon Storm mountain bike which was found at the scene and has been a main focus of garda appeals for information to the public, may have fingerprints and DNA belonging to the suspect on it.
It has also emerged that Ashling's killer lunged at another young schoolteacher and a garda's wife as they tried to go to her aid during the fatal assault on Wednesday.