Primary schools may have to have a morning and an afternoon session when they reopen, according to the INTO.
The Health Minister says he has discussed the possibility of reopening primary schools, even for just one day a week.
Latest figures show 610 people have now died from Covid-19, with 39 deaths announced yesterday.
The number of confirmed cases of the virus in Ireland has reached 15,251 as another 493 new cases of the virus have been found in the Republic yesterday by Irish and German labs.
General secretary of the INTO John Boyle says the school day may have to be staggered because of class sizes.
“We have the largest classes in Europe - 30 children in a class,” he said.
“Obviously they’d have about 60 square metres to play around with, in the classroom.
“I couldn’t imagine initially that everybody would be back together.
“Perhaps if half the class came in in the morning and the other half came in in the afternoon.
“We could talk about those things in the discussions.”
Meanwhile, most Irish teenagers are hopeful for the future after Covid-19.
New research by Young Social Innovators shows almost 70% of 16 to 19 year-olds are optimistic society will change for the better.
Over half of them are feeling anxious, stressed or depressed during the pandemic.