There has been little expectation the Junior Cycle June exams would take place because of the public health landscape.
There is a widespread view among education stakeholders that it would be too much to run both sets of exams together in June - on health and safety grounds.
Each set of exams involves around 60,000 students and many schools would have several hundred candidates.
Education Minister Norma Foley said the Junior Cycle exams would be on the table in the current discussions but they have not featured.
Tonight, the TUI has called on the minister to cancel them.
“The TUI is of the view that the State Examination Commission (SEC) Junior Cycle exams cannot proceed this year and is calling on the Minister to confirm this to students, teachers and parents.