The Minister for Education, Mr Dempsey, is expected to back a new student loan scheme, rather than the return of up-front college fees, as part of his plans to widen third-level access.
Regardless of which option is brought in, it is accepted that the current system of free third-level education for middle and upper income groups is set to end from September.
Under the loan system, students would effectively be "loaned" the cost of their college fees. They would be asked to repay the loan once they achieve a certain income after graduation.
Department of Education officials are examining an Australian-style scheme where students are asked to repay some ¤2,000 per year for arts courses, ¤3,000 for maths, science and computer courses, and ¤4,000 for law and medicine courses.
In Australia, graduates pay between 3 per cent and 6 per cent of their annual income, depending on their total earnings, until the cost of their loan is covered.
Poorer students and those who are earning less than about ¤15,000 per year are exempt from any charges. Discounts may apply where fees are paid up front.
Sources say that while the return of "upfront" fees remains an option, some kind of loan scheme is more likely.
One source said: "What is clear is that the current system of no fees and no loans is over from next September."
Mr Dempsey's review of third-level funding received a significant boost this weekend when the Taoiseach, Mr Ahern, said the Minister was "leading the way" in developing a new more equitable base for Irish education.
He also noted the "striking" benefit of a third-level education as "graduates enjoy a premium of up to 57 per cent in their pay packets".
Mr Dempsey first signalled the possible return of fees for "those who can afford them" in an Irish Times interview last year. Officials are finalising a review of third-level funding, which will present the Minister with a series of options.
It is likely to propose radical reform of the higher education grants system. Some would like to see control taken away from local authorities and handed over to the Department of Social, Community and Family Affairs, who have greater experience of means-testing. Agreement has to be reached on any new system.
Addressing Ógra Fianna Fáil in Portlaoise, Mr Ahern said: "If we want to break cycles of disadvantage and open up opportunity for all, we have to broaden participation in universities and institutes."
He said: "We need now to step up activity. I do not believe this can be achieved through simply pouring more money into the same approaches. Support has to be targeted at those most in need, and it has to be at a level which really supports them in college."
Last year, in the run-in to the Nice referendum, Mr Ahern was circumspect on the level of his support for new fees or student loans. However, his strong public support for his Cabinet colleague at the weekend is believed to clear the ground for radical changes in student funding.