Oxford University's vice-chancellor has questioned the long-term sustainability of the £9,000 fixed upper limit for tuition fees.
Andrew Hamilton told a university gathering the real cost of an Oxford undergraduate course was £16,000.
He asked how a "market" in higher education could operate if everything "regardless of content and quality, is the same price".
The university faced an annual funding gap of £70m, said Prof Hamilton.
He argued that different types of institutions should be able to charge different levels of fees.
"Given the great diversity of the institutions in our higher education system, the notion of different universities charging significantly different amounts, doesn't feel inherently unnatural.
"It is the current situation that seems out of kilter. What matters surely is that an institution's charges are clearly aligned with what it offers and that they are demonstrably not a barrier to student access."
A university spokesman said that the speech was not proposing that students would have to pay fees of £16,000 per year to bridge the shortfall.
But Prof Hamilton suggested a "system of tuition charges more closely related to the true cost", with the "strongest guarantees" of support for poorer students.
Prof Hamilton argued that there needed to be a more sustainable funding model for universities where £9,000 did not cover their costs.
He had heard that some universities were "doing very nicely thank you" with fees of £9,000.
"That may or may not be the case for them, but one thing I am quite sure about is that it doesn't add up for Oxford, where the new regime of increased tuition charges for students, but greatly reduced government spending on teaching, have done little to change the basic financial equation."
Along with ideas such as increasing philanthropic donations, he floated the idea of raising funds through issuing bonds to investors.
The raising of tuition fees to £9,000 was a highly controversial measure, prompting violent protests and occupations, in the biggest upsurge of student activism for decades.
Academics at the University of Oxford passed a symbolic motion of no confidence in Universities Minister David Willetts and his higher education funding reforms.
But with the funding changes in place, the speech on Tuesday by Prof Hamilton shows there are still far-reaching financial questions for such leading institutions.
How can they compete on an international stage with better-funded rivals?
Harvard University's financial figures, released last month, showed the US university has an endowment that has grown to $32.7bn (£20.3bn).
A fundraising drive by Harvard, launched last month, aims to raise an additional $6.5bn (£4bn).
Last year, Oxford hailed the donation of £75m as "the largest such benefaction for undergraduate financial support in European university history".
Responding to the speech, Sally Hunt, general secretary of the UCU lecturers' union said: "Prof Hamilton should perhaps be applauded for going after one of the rawest nerves in politics to try and get higher education funding back in the spotlight - something we fear no party will be keen to do this side of the general election.
"However, higher university fees are not what this country needs.
"Prof Hamilton is correct to say our universities need more funding - we invest just 1.4% of GDP on higher education, compared to an international average of 1.7%.
"However, he is wrong to argue that students should pick up tab when we already have the most expensive fees in Europe."