The Association of Secondary Teachers Ireland (ASTI) has said the State exams should proceed this summer, with modified papers.
It comes as talks will take place later between ministers and senior education officials on the exams.
The Government is also hopeful a phased return to schools can take place over the next couple of weeks.
Ann Piggott, president of the ASTI, told Newstalk Breakfast their preference is for "modified" Leaving Certificate papers, since students have missed so much school.
"It is our preference that we would have a Leaving Cert - at this stage, we're fully aware that people have missed a lot of face-to-face teaching.
"So we would like modified papers to the point where it would be doable, it wouldn't cause too much anxiety, there would be plenty of choice for students to omit certain areas of the curriculum as they require".
"We would certainly favour the traditional, written exam - that would be our preference".
But she said issues could arise if students got to choose between sitting the exam or getting predicted grades.
"The problem with a choice like that is there isn't an equivalence in terms of a choice: they're two very different paths.
"One would involve a grade being given to students, and from our perspective... we would be worried that if a grade is given, does that mean then that motivation is gone? That students would not remain at school in May?
"What would teachers do if they're teaching for the Leaving Cert as well? If the choice is given, you will certainly have a huge cohort of students as well who will choose the traditional exam.
"So that would make it very difficult for us".
And she said they would "certainly hope" that the country is weeks away from a phased return of children to schools.
"The numbers have gotten down, they were huge - they were over 8,000 - they dipped to 928.
"I know they've gone up again, but we would certainly hope as the weeks go on that they would come down to levels where everybody could be back at school".
Asked if there would be a difficultly with schools being open if the the numbers fall, she said: "At least if the numbers are going down, we would have a starting point".
"We would like to know that they would be safe in terms of new variants, we would like risk assessment, we would like contact tracing to continue.
"But certainly if the numbers are going down, our members are more than ready to go back to school".
It comes after the Irish Second-Level Students' Union called for students to be given a choice between calculated grades or sitting the exams.
On Sunday, union president Ruben Murray told Newstalk Breakfast with Susan Keogh: "We did a survey of over 25,000 students and one of the things that came back very clearly was that the communication from the Department [of Education] is not strong enough and it needs to improve," he said.
"Students have no idea what's going to happen with their exams, there hasn't been that clarity there.
"Students want a choice, after the disruption they've faced they want a choice between sitting the exams, scaled-down, or calculated grades."
