A university chief has launched a pre-emptive strike ahead of the Government's overhaul of funding, claiming that both tuition fees and the teaching grant should increase.
The £9,250 per year that students are currently charged is no longer sufficient and courses are being run at a loss, according to the chief executive of the Russell Group.
Dr Tim Bradshaw's remarks come as ministers prepare a response to an official review of higher education which recommended last year that tuition fees should be capped at £7,500.
Philip Augur, who led the review, has since rowed back on the idea claiming that disruption caused by the pandemic would mean that such a fee cut would be "too destabilising" for the sector.
But it is understood that there are some in the Treasury who are still pushing for a tuition fee cut ahead of the spending review next month.
"The question of a tuition fee cut is still up in the air," a source said. "There are some who think universities got off scot free in the last austerity round".
The head of the Russell Group, which represents the country's 24 most prestigious institutions including Oxford and Cambridge, said that tuition fees no longer cover the full cost of many courses.
Universities currently receive funds through tuition fees as well as from an annual teaching grant where the Government allocates extra money for 'high cost' subjects.
Dr Bradshaw said that degrees in subjects like engineering, chemistry and physics cost an extra £1,750 per student per year on top of tuition fees.
"Something that has changed recently is that even the social sciences are being taught at a deficit, so there is no flexibility," he said, explaining that degrees in subjects like history and archeology are now being run at a £700 loss per student per year.
He said that current funding levels for universities are not feasible in the long-term and that either tuition fees or the teaching grant must be raised.
"We need overall sustainable funding and a cast iron guarantee that the funding we get per student isn't going to fall below where we have it now. And ideally what we need is that the grants plus loan plus fees element increases because of the deficits that we're currently facing," Dr Bradshaw said.
"Universities are having to invest a huge amount more in their Covid response - digital learning, mental health and other things."
The suggestion that tuition fees should be raised will be greeted with surprise by those who believe that students' university experience during the pandemic has been worse than expected and that graduating into a recession with even more debt will add further strain to their finances.
Earlier this year the Government rejected universities' plea for a £2 billion bailout after vice-Chancellors claimed that without a cash injection some institutions would face "financial failure" due to the coronavirus pandemic.
Instead, the Education Secretary announced in May that universities will be able to access £100 million of research funding as well as £2.6 billion of tuition fees a few months earlier than they would otherwise have been able to.
But following the Government U-turn on A-level results in August, universities successfully lobbied ministers for an additional £20 million as part of a deal to ensure that places could be found for the thousands of extra students who met the terms of their offer.
Dr Bradshaw said universities should be given "more credit" by ministers for their achievements this year adding that they have "pulled it out the bag".
"People forget that we completely changed the assessment system at the end of last academic year," he said. "We have really invested in the quality of the blended learning experience."
A Government spokesperson said: “We understand this has been a challenging time which is why we have introduced a package of measures to stabilise the sector, help universities manage their finances and safeguard students.
“We are considering the recommendations of the Augar Report as part of the Review of Post-18 Education and Funding, and plan to respond at the Comprehensive Spending Review.”