England's top universities could have turned into private institutions if the government dropped plans to increase tuition fees, Vince Cable has said.
The business secretary told the Girls' Schools Association (GSA) that he could make no guarantees about the future.
He said Oxford, Cambridge and the London School of Economics (LSE) could be among those tempted to go private.
The LSE and Cambridge University have previously rejected claims they were considering the move.
Universities are to be allowed to charge up to £9,000 a year for courses although the government expects most of them to charge about £6,000.
MPs are expected to vote on the proposal before the end of the year.
During his speech at the GSA conference in Manchester, Mr Cable said: "One of the reasons were are doing this is precisely to head off Oxford, Cambridge, London School of Economics, University College London and a few others from going private, because if we had not opened up the system in the way we have, they would have had a very strong incentive to do so."
"Whether we shall head them off, I don't know."
He added that Lord Browne's independent review of university funding in England, published last month, had proposed that universities should be able to charge unlimited fees.
But he said that the government had rejected this out of consideration for how it would affect those from poorer backgrounds.
Mr Cable, a former Cambridge University student, said he did not think his alma mater would become privatised as the new proposals would benefit them, but he said he would "very much regret it" if the university did make that choice.
He said: "I find it it difficult somehow to imagine Oxbridge opting out, because they have got all these different colleges, they've got different institutions, how are they going to manage that?
"It's a little bit like bankers who say if you're going to put some kind of tax on us we'll run away to Singapore."
"Universities have been playing this game with us - let us have unlimited caps or we'll privatise. I don't believe it.
"I think what we're proposing is a fair settlement which will provide them with enough income to provide high quality education and which is also fair to the pupils."
Mr Cable said the government was unable to help universities that were failing.
He said: "We already have a lot of universities that are effectively broke. If they were in the private sector they would have been filing for bankruptcy. Various arrangements have been cobbled together to keep them going, and we can't continue to do that."
He said students were no different to bank depositors and the government was thinking about how to manage institutions that failed.
"If a bank goes bust, it has got to be allowed to close, not to its depositors, the depositors have got to be protected. The depositors are the students.
"So if somebody signs up for a university degree course and the university then goes bust, those students must have the right to continue their higher education.
"But the institution and its management could well disappear and many of those institutions could change and become further education colleges, could be taken over by another education provider, so there will be change."
Last month, Professor Andrew Hamilton, the vice chancellor of Oxford University, said it cost about £16,000 a year to teach an undergraduate there, with half of that coming from tuition fees and public funding.
Students across the country have taken part in demonstrations against the planned increases.