Chief Supt David Sheahan said they cannot say if Marco Velocci stayed overnight on Monday night with his former partner.
He said it was a very complex investigation and they have yet to speak to Ms Power who underwent further surgery at University Hospital Limerick for serious arm injuries.
Chief Supt Sheahan said: “We cannot confirm any matters related to the movements of Mr Velocci other than we believe he called to the home of Ms Power the night before. We cannot confirm if he stayed overnight.
“Jodie Power resided at Glebe, Oola with Marco’s son Alex and another of her children aged nine months.”
Chief Supt Sheahan said one of their lines of inquiry centred on reports that Marco stayed at Ms Power’s house the night before.
Chief Supt Sheahan said: “We are trying to get correct information.”
It has been established from local information that the couple were seen out walking with their son on Monday night.
Meanwhile, a local politician has pleaded for the families of Marco Velocci and his son to be given time to grieve.
Alex’s mother, Jodi Power, 26, suffered a broken arm and a number of stab wounds when Mr Velocci, aged 28, forcibly abducted Alex from her home at Glebe, Oola, on Tuesday, minutes before he crashed his car into an artic truck, killing himself and the child.
The deputy mayor of Limerick city and county said the community in Oola must now be given space and time to try and come to terms with the tragedy, which has cast a dark shadow over the entire community.
Fianna Fáil councillor Noel Gleeson, who represents the Oola area on Limerick City and County Council, said people are so saddened and shocked they are finding it hard even to talk among themselves about the events of this week.
Mr Gleeson said: “This is a fine community and the people will gather and support each other in solidarity over the coming days and weeks. There has been a lot of media coverage of what happened. But the media must now stand back and allow the community deal with this tragedy with dignity and space.
“The wishes of the bereaved must be uppermost in all our minds and if they request privacy in the coming days this must be respected.
“I would appeal to the media to respect whatever the wishes of the families are. There is an investigation under way by the gardaí and they are the people charged with this job.
“The wider general public, in my view, now know as much as they need know. Many people are suffering great emotional pain and they don’t want people trespassing on their grief.”
Meanwhile, the bodies of Alex and Mr Velocci are expected to be released to their families today following the completion of autopsies at University Hospital Limerick.
The postmortems were carried out yesterday by assistant State pathologist, Louise Mulligan.
Funeral arrangements can be made once the bodies are brought from the morgue at the hospital.
Garda liaison officers have been appointed to provide support to the families and to arrange counselling.
Senior gardaí held a case conference at Bruff Garda Station.
While gardaí are viewing the crash as a suspected murder suicide, it cannot be officially designated as such until all the various forensic aspects of the investigation are finalised.
These include toxicology tests of blood samples taken from Mr Velocci’s body and these can take up to a month to conclude.
Prayers have been said at the local parish church in Oola and the church in neighbouring Solohead, where Ms Power’s family resides.
Family and friends have been visiting Ms Power in hospital and she may be allowed home today.
As part of the garda investigation, social media material linked to Mr Velocci is being analysed to see if there was any indication of any intention to harm himself or anybody else.
A number of people who witnessed the accident have been interviewed by gardaí.
All statements will be compiled for a coroner’s inquest and this will officially determine the cause of the two deaths.