There are plans for a new Gaelscoil in Cavan town.
CMETB and the Department of Education are examining a site at the former Dún Uí Neill army barracks.
Ownership of the barracks was transferred to the organisation after it closed in 2011.
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A spokesperson for CMETB says board members "discussed the possibility of locating a permanent school building for Gaelscoil Bhreifne on the lands at Cavan Barracks".
It says the Department of Education has written to the board seeking to explore the possibility.
The army barracks site is expected to become the permanent home of Cavan Institute in the coming years if the plans are approved by the Department.
