The Teachers' Union of Ireland says they have concerns about the lack of clarity regarding the vaccine priority list.
It comes after the Minister for Health asked his department to examine the possibility of vaccinating younger age groups against COVID-19 earlier to reduce transmission of the virus.
Stephen Donnelly is proposing that people aged 18 to 30 would get their inoculations before those aged 30 to 50, once people in their 60s are vaccinated.
The CEO of the HSE said that he is not aware of any plans to change the vaccine priority list.
However, Paul Reid added that the health service is ready to make adjustments from the aged based system if asked to do so by Government.
It is just over two weeks since the Government made changes to the rollout, removing certain professions from the list to prioritise older people first.
The move sparked outrage from teaching unions who threatened strike action over the change.
President of the TUI, Martin Marjoram, told Newstalk Breakfast with Susan Keogh that the last U-turn was badly communicated to them.
"We're still coming to terms with the U-turn over vaccine allocation groups and the way this was very badly communicated to us, which was effectively through leaks and very angry and distressed texts from our members," he said.
"So for more speculation, and it looks like there may be some logical reason behind it, but again it certainly isn't emerging in any discussions with us in advance.
"We do have concerns about the leaking, the speculation, the kite-flying at times and the general way the communication happens around these things, as well as the lack of clarity and the fact that plans seem to change so quickly."
Mr Marjoram said that at the union's recent congress, there was "significant disquiet at the de-prioritisation of education".
He added that if there is a return to the vaccine programme being rolled out on the basis of occupational settings, the education sector would welcome it.
A recent meeting with public health officials was very positive, he said, but unions are hoping to have further discussions with Government.
"We have ongoing concerns about special schools, which are very different from standard classrooms," Mr Marjoram explained.
"There are those who have been vaccinated, partly because they're employed by the HSE and other teachers and SNAs have not been vaccinated even though they're in a very similar setting.
"Anomalies like that really cause grave disquiet among those who are going into those settings."
If the vaccine priority list is altered to vaccinate younger people first, he added that teachers' unions will continue to seek a meeting with decision-makers to discuss the "glaring anomalies" with the programme, as well as how those in education were treated with regard to the recent announcement on moving to an age-based system.
"I think we desperately need some indication of the actual timetable for this," Mr Marjoram stated.
"As things stand, it does look as though we may well be returning to school in September without all of our teachers having been fully vaccinated.
"The level of disruption to education that happens because of any outbreaks or any testing that needs to be done in schools is something that we're concerned about, particularly the extent to which the education of so many students is interrupted over the last few months.
Mr Marjoram said unions will "continue to seek the clarity" they need, as well as asking for a "more orderly way" of decisions being made and communicated, rather than. through speculation and leaks.