The Minister for Education, Mr Dempsey, has said he has no objection to third-level institutions leaving the State sector and becoming privately owned.
Reacting to a Higher Education Authority (HEA) submission, Mr Dempsey said his one concern would be to make sure that students from disadvantaged backgrounds could gain places in the private institutions.
"I have no objection on a personal basis or on principle to a college, if they want, going out of the public system and becoming private colleges.
"The one caveat I would have to put in, though, is there would have to be systems in place to ensure that people from disadvantaged backgrounds would be able to get into them. So there would have to be scholarships and bursaries like in the American system."
Mr Dempsey, speaking on RTÉ radio, was reacting to a HEA submission which suggested State-owned colleges could "evolve into" private institutions. The submission has been passed to the Paris-based OECD and the Minister.
The HEA has stressed that the private institutions would be not-for-profit. Its chairman, Dr Don Thornhill, a former secretary general of the Department of Education, said certain leading universities should be given the opportunity to go private if they wanted. He pointed out that US colleges like Harvard and Yale were in private hands.
SIPTU's education branch said the idea made no sense. Its education branch president, Ms Marnie Holborow, said: "It is another knee-jerk reaction to the privatisation craze on the part of the Higher Education Authority. Irish universities have played a major role in supplying graduates for our knowledge-based economy. This is why the State provides 79.2 per cent of university funding.
"The models are Harvard and Yale universities in the United States. Student undergraduate fees at Harvard currently stand at $40,450 a year, and $37,000 a year at Yale - over 10 times what an Irish student would expect to pay.
"Staff work longer hours, have fewer holidays and are often on temporary contracts. In the US, the government provides only 34 per cent of university funding, whereas in some European countries it is over 90 per cent."
The Labour Party education spokeswoman, Ms Jan O'Sullivan, said the proposals represented "nothing more than an attempt to reintroduce student fees by the back door.
"These 'Harvard-style' proposals will see points requirements for Irish students to gain entry to universities shoot-up as more and more places will be open to international competition. Just at the time where we are witnessing a levelling-off in the points needed for many courses, the Government will be making it more difficult for teenagers to get to university."