The Health Service Executive placed an ad in local media last week, urgently appealing for parents to come forward for the three children "so that they can grow up together".
The emotive ad describes the three children -- aged five, four, and one-and-a-half years -- and tells of their talents and hobbies.
"Katie is a real little girl who loves dressing up and having her hair done. She loves school and has got trophies for her reading which she is delighted about," the ad says.
A spokesperson for the HSE said it could not comment on the circumstances surrounding the specific family, but she said the HSE was always on the lookout for foster parents.
"The HSE does from time to time advertise for foster carers for children if it doesn't have a suitable family.
"This might prompt other parents to get in touch with the HSE in relation to foster care as well," she said.
Meanwhile, Liam Cullen, Director of Irish Foster Care Association, said the HSE was under pressure to find new foster parents because most of its energies are tied up with catching up on the backlog of cases which did not meet the demands of a Health Information and Quality Authority (HIQA) report released last week.
The HIQA report found that foster parents were still not being adequately assessed, vetted and approved by the HSE.
It also found a "significant failure" by the HSE to provide evidence that it was adequately monitoring all children placed in foster care.
Mr Cullen said: "Some parts of the country are struggling to recruit foster carers because of a recent HIQA report into the lack of assessment of foster carers.
"Assessments were not carried out in respect of children placed in foster families. And the HSE is trying to catch up on that, and it's curtailing their ability to recruit new foster parents.
"The HSE have held meetings around the country, and they've had stalls in farmer's markets to promote fostering as an option."
However, he added that there was a constant need for a recruitment of foster carers, while the HSE can have some families which they can call upon when multiple numbers of siblings need to be fostered.
"Foster care teams should constantly be trying to recruit new families," he said.