The recording was made during an interview with a journalist in which Rhonda Tyson appealed to Kyran's mother Dayla, who was also missing at the time, to make contact with her.
Dayla was found alive in Great Britain without Kyran.
Some of the information provided by Ms Tyson in the interview contradicts Garda statements surrounding the last time Kyran was seen.
Gardaí are now in possession of the tape as part of the investigation.
Drogheda Life journalist Andrew Spearman said he had a "nodding acquaintanceship" with Ms Tyson prior to their interview.
When Gardaí launched a murder investigation weeks after the recording was made, Mr Spearman said he was "gobsmacked".
"I was shocked to the core. How could that be?
"I don't often stay awake at night thinking about things, but I did with this because, you know, either she was lying through her teeth to me, or the guards are wrong."
Spotlight approached Ms Tyson for a comment but she declined to respond.
"The case of Kyran Durnin is deeply upsetting and as a parent I am horrified to think that a child can disappear and that it could go unnoticed," Mr Givan said.
"Kyran's case is subject to An Garda Síochána investigation and we need to understand what went wrong in this situation."
An internal review of Tusla's interactions with Kyran's family has been carried out, but has not been made public, in consultation with gardaí.
Tusla told Spotlight that although Kyran was not in its care, significant efforts were made by staff to provide further support to the family in 2021/22.
It also said no referral was received from Kyran's school in relation to concerns about his welfare or attendance.
The Garda Commissioner, Drew Harris, previously said he had never seen a case like this in his 40-year career in policing on both sides of the border.
Ireland's Special Rapporteur on Child Protection, Caoilfhionn Gallagher KC, is calling for a full public inquiry to establish how Kyran went missing for two years without anyone noticing.
"The case is utterly horrifying. This is a child who's completely vanished off the face of the planet," she told Spotlight.
Ms Gallagher said this case should be a "watershed moment" for child protection in Ireland.
"[It] seems to me there has got to be a robust independent inquiry, a public inquiry, which looks at the broader non-criminal issues and looks at how on earth this can have happened, and fundamentally looks at what needs to change in Ireland's child protection systems to ensure that this never happens again."
She added: "It seems to me that although we don't yet know the detail, we do know that this was a child who was fundamentally very badly failed, and it seems likely was failed by multiple agencies and potentially by multiple individuals."