The standing committee of Association of Secondary Teachers Ireland (ASTI) is meeting to discuss the outcome of talks with school managers this morning.
A statement from the teachers' union is expected later this evening.
ASTI representatives met members of the Joint Managerial Body earlier today in a final push to try to solve the row over teachers' supervision. The talks ended without agreement.
The JMB has also held meetings this evening, but has yet to make a statement.
The dispute centres on a demand by ASTI that its members be paid for being on call for supervision duties.
A meeting on Monday at the Department of Education between ASTI and the Minister, Mr Dempsey, broke down after only an hour.
A deal brokered by the three teaching unions and the Department last year calls for teachers to be available for 37 hours of supervision per school year.
The Irish National Teachers' Organisation and the Teachers' Union of Ireland have agreed to the deal.
ASTI members voted by nearly three to two before Christmas to accept the deal, which would see them being paid €37 per hour for supervision. The standing committee will discuss this afternoon whether or not to hold a fresh ballot.
ASTI is insisting its members be paid for being on call, whether they are required to supervise students or not. The union has offered to have its members available for 66 minutes per week - 37 hours over the course of the school term.
Mr Dempsey has ruled out payments for being on call, saying teachers will only be paid for hours actually worked.
It is understood the Department and the Joint Managerial Body (JMB) is seeking a more flexible approach from teachers, whereby their hours can be carried over from week to week if they are not called to perform supervision duties.
