It cost the Department for the Economy almost £5m to educate further education (FE) students from the Republic of Ireland last year, the BBC has learnt.
The executive had previously sought compensation for the cost of educating FE students from the Republic in NI.
The former further education minister Stephen Farry made the demand to the Republic's Department of Education and Skills in 2014 and 2015.
No compensation was paid as that would have breached European legislation.
In a statement to the BBC, the department said that it paid for almost 2,500 students from the Republic of Ireland to be taught in Northern Ireland in 2015/16.
It said there were "2,471 enrolments by students from the Republic of Ireland who were funded through the FE block grant in the six Northern Ireland FE colleges, at a cost of £4.8m".
According to official figures, the majority of those students cross the border from Donegal to be educated at North West Regional College.
'Not fulfilling their duty'
In 2014, the annual cost of educating students from the Republic in Northern Ireland was higher, estimated at £7m.
This led Mr Farry to tell a Stormont committee that "the government of Ireland are not fulfilling their duty to provide for the training and education of their young people, and we are, effectively, picking up the pieces".
In their statement to the BBC, the Department for the Economy said that had led Mr Farry to make an official approach to the Republic of Ireland for compensation.
"On 5 December 2014, Minister Farry raised the issue of RoI providing a contribution to offset the disproportionate cost of funding RoI students in the north west."
"However, no agreement was reached on the issue.
"This was followed up by a letter from Stephen Farry to Jan O'Sullivan in January 2015."
Jan O'Sullivan was the Republic's higher education minister in 2014-15, a post now held by Mary Mitchell O'Connor.
According to a report in the Sunday Business Post, Ms Mitchell O'Connor was briefed on the cross-border compensation issue when she took office in June 2017.
A joint-working group has been established by the two governments to examine the movement of students across the border and meets once a year.
Students from the Republic of Ireland are the largest group of students from outside Northern Ireland educated at FE colleges here.
However, they make up only a small proportion of the overall FE student population, which has been falling.
National Union of Students USI President Olivia Potter-Hughes said cross-border study was beneficial for cross-border relations and helped maximised students' career opportunities.
"It is also important that the significant benefits of cross-border mobility and EU mobility are realised and maximised," she said.
"It is crucial in this time of massive uncertainty that government provides guarantees on that protect Erasmus+ and cross-border and EU-wide student mobility."
In 2015/16, 82,818 students overall attended FE colleges in Northern Ireland.
The Republic's Department of Education and Skills (DES) estimate that the number of Northern Irish students attending FE colleges in RoI is very small.
"Data made available to the department suggest a modest take-up each year (in double digit figures) by Northern Ireland students of further education and training places in Ireland," it said.
"The movement of students across borders is one aspect of a broad range of social and economic relationships between EU member states.
"An approach based on reciprocal funding arrangements would be inconsistent with that position and EU rules on free movement of people."