It stated: "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".
The British government had proposed using technology such as surveillance cameras to allow continued free trade between the north and south of the island.
Irish Prime Minister Leo Varadkar has said Ireland is "not going to design a border for the Brexiteers".
On Friday, Irish foreign minister Simon Coveney also rejected the plans for a technical solution and called on the British government to come up with other options to deal with the border issue. "That is not going to work", Irish Foreign Minister Simon Coveney told a meeting of European Union foreign affairs ministers as cited by The Telegraph.
Ireland has instead been suggesting that customs and immigration policies would be enforced at air and sea ports, instead of on land.
Sources told the paper that Mr Varadkar thinks a land border would jeopardise the peace process.
The current border between the Irish Republic, a member of the European Union, and the British province of Northern Ireland would become the only land frontier between the United Kingdom and the EU once Britain left the bloc in early 2019.
The DUP, needed by British Prime Minister Theresa May to prop up her minority administration in the House of Commons, has ruled out the suggestion of a sea border post Brexit. "What we are saying is that there is an onus on the United Kingdom to come up with imaginative and if necessary unique solutions", Coveney told national broadcaster RTE.More news: BT Forced to Pay Out to Avoid Court Battle Over Italian Scandal
More news: Shah Rukh Khan: Pictures of his flawless look alike
More news: European Union executive to start legal action against Poland over judiciary reform
Asked if the position risked angering unionists and supporters of Brexit in Britain, Varadkar suggested that it was Ireland that had the right to be angry at Britain's decision to renage on earlier agreements.
Leo Varadkar says Ireland will not help to design a border it does not want.
A spokesman for the Department of Exiting the European Union said the Government aims for "as frictionless and seamless a border as possible" and wants no new barriers.
Any hindrance to cross-border trade would hit Northern Ireland harder.
About 30,000 people cross the current, invisible frontier each day for work and many farms straddle both sides of the border.
"It's the United Kingdom, it's Britain that has chose to leave and if they want to put forward smart solutions, technological solutions for borders of the future and all of that that's up to them", he said. "Dublin really needs to understand that the proposition is absurd, it's unconstitutional", DUP MP Jeffrey Donaldson told BBC Radio Friday.
"There is no realistic solution that has been put forward", he said.
"It is our priority to deliver a practical solution, that recognises the unique social, political and economic circumstances of the border".