Three teacher unions have backed a motion that could lead to industrial action.
The INTO, TUI and ASTI members voted in favour of the motion following a change to the vaccine priority list.
Last week the list was altered so a person will be in line to receive a vaccine based on their age rather than their profession.
Education Minister Norma Foley told the INTO's conference yesterday that she understands their disappointment.
However, she said new evidence shows age is the strongest predictor of whether a person who contracts Covid-19 will be admitted to hospital or die.
This morning, the Minister said she was hopeful that teachers will not strike in the short term over the decision.
She said "If they take that action, that would be for much later in the year. We are currently in April. I think that's a very long way off. I think we'd be putting the cart before the horse at this stage to consider anything that might happen in the future and is not happening currently.
Speaking this afternoon, Taoiseach Micheal Martin says there are no plans to change the vaccine rollout list.