The plight of the Connors Traveller family, camped on the Naas dual carriageway near Rathcoole, is being investigated by South Dublin County Council.
The local authority, however, was unable to confirm whether the family was on its "assessment of need" priority list.
Officials at the council's Travellers' accommodation section could not readily identify the Connors as one of their client families, despite the report in this newspaper yesterday of the chronic conditions being endured by Ms Brigid Connors, her two sons, Miley (10) and Tommy (8), and her partner.
Ms Connors is awaiting the birth of her third child on Christmas Eve.
The family told The Irish Times that their leaking caravan had been parked on the present site for two weeks and their living conditions were very bad.
"We won't say at this stage what the position is or comment on our attitude to them until we know whether we have a duty of care or know them at all," said Mr Mick Fagan, the council's senior administrative officer with responsibility for Travellers.
He would be investigating the situation, he said.
The Department of Education said it was investigating the circumstances of the Connors children with regard to providing schooling for them.