The Minister for Health, Simon Harris, has said he personally believes there would be health and wellbeing benefits to getting children back to school, even in a partial capacity.
He said there may be a need to focus on exam students or on students with special needs.
Mr Harris said he would love to see schools come back and government would have a number of options to consider if it got to a point where that option could safely be implemented.
But he stressed this would only happen if the National Public Health Emergency Team (NPHET) deemed it safe to do so.
Dr Cillian de Gascún, the head of the National Virus Reference Laboratory and chair of the expert advisory group on the coronavirus, said the idea of schooling one day a week would allow students to return to some sort of normality without mass gatherings.
This would also allow for physical distancing.
"We are conscious that sixth year students are trying to prepare for the Leaving Cert in very difficult circumstances. Rather than trying to bring everyone back, we might look at that group and see if we can do something for them."
Dr de Gascún said it "would be nice to lift" some restrictions after 5 May but stressed that sufficient testing capacity and contact tracing capacity need to be in place for that to happen.
He said a decision as to whether or not the Leaving Cert exam would go ahead was for the Department of Education and not for NPHET but he would welcome "anything we can do to support" students.
It is understood that it is unlikely the re-opening of schools would happen immediately if restrictions were eased on 5 May. But a pathway towards some partial reopening of schools may become clearer at that stage.
Dr de Gascún said any changes in restrictions will be very phased and controlled. "Life will not be returning to normal in the short term."