One of the country's main secondary school teachers' unions expects schools to reopen after the mid-term break, but has warned that teachers are "very fearful".
Speaking on RTÉ's Morning Ireland, the President of the Association of Secondary Teachers in Ireland said they would like schools to be open "in a very safe way".
Talks have been taking place between the HSE, the Department of Education and teachers' unions over how to tackle Covid-19 infections in schools.
A revamped contact-tracing system is due to be in place when schools reopen after the mid-term break.
A public health risk assessment takes place as soon as a case occurs in a school, which Ann Piggott said her members would like to know more about.
"We'd like to have more confidence in it," she said.
"We'd like to ensure that all details are out in the open for everybody to know. Because even if there is a case in schools, teachers currently are dependent on rumours.
"They would like to know for a fact - is there one case, are there three cases, how much at risk are teachers and students themselves?"
Ms Piggott said they are worried about the amount of time it takes to identify a positive case, and that teachers have asked from the beginning for rapid testing to take place in schools.
She said that if tests could be returned within 24 hours "that would be much better" than the current waiting time.
"It can take two to four days for the results to come back and then the contact tracing after that is very slow as well, perhaps another four days", she said.
"We would welcome any rapid testing but we would certainly like it to be accurate."