Graduates in England will pay significantly more for their degrees, a review of higher education funding is expected to say.
A report by Lord Browne is likely to recommend removing the fees cap, allowing institutions to charge what students are prepared to pay.
The current cap is £3,290 a year.
Many universities are expected to charge between £6,000 and £7,000 annually, but they will have the option to charge more.
The recommendation will be politically difficult for coalition partners the Liberal Democrats, as many of them - including leader and Deputy Prime Minister Nick Clegg and Business Secretary Vince Cable - have signed a pledge to oppose any increase in fees.
Other recommendations in Lord Browne's report include increasing the salary at which graduates in England start to repay their tuition fees from £15,000 to £21,000.
Ahead of the review's publication, ministers also outlined plans to help poorer families afford a university education through increasing grants and loans for poorer students.
Ministers have been trying to reach a compromise that will be progressive enough to secure Lib Dem backing.
Prime Minister David Cameron told reporters at Downing Street on Monday the issue was "very difficult" for the coalition.
He said: "Everybody has to compromise because the truth is that we all want the same thing."
Business Secretary Vince Cable, who has responsible for higher education in England, outlined his response to the review at what was described as a productive and constructive meeting of Lib Dem MPs on Monday night.
Lib Dem rebels
There was no sign of full-scale rebellion, but a handful of those present indicated they may vote against the proposals when they come before Parliament in a few weeks, reported BBC political correspondent Mike Sergeant.
The National Union of Students told the Guardian newspaper that nearly 30 Lib Dem MPs were prepared to rebel.
MP Greg Mulholland said he would be among them. "I am trying to make it clear to government that we simply wouldn't accept a rise in tuition fees. Our position on tuition fees resonated with people and was a very important policy area," he told the Guardian.
The government is also considering asking all but the poorest graduates in England to pay a higher rate of interest on their student loans.
Currently all graduates pay a low interest rate, linked to the base rate, on their tuition fee and maintenance loans.
Currently graduates who took loans out after 1998 pay interest rates of 1.5% - but this was only introduced this September - the previous year it was fixed at 0% for that year.
It is also expected that there would also be pressure on universities to provide more bursaries.
Universities would be able to keep all of tuition fees up to about £6,000 or £7,000, but beyond that point they would only be able to keep a diminishing proportion of the fee paid by students.
This would mean more than doubling the current tuition fee of £3,290. And if the major cuts expected in the comprehensive spending review go ahead, it could mean few extra resources for a struggling university sector.
Andy Westwood, chief executive of GuildHE which represents some universities said: "Not all higher education institutions will be able to charge more for many of their courses.
"Lifting the cap on fees could be very damaging for them if coupled with across-the-board cuts in public funding for certain subjects."
Former BP boss Lord Browne's review of fees relates only to England, but its recommendations will be watched closely by university vice-chancellors in the other nations who are facing the same funding conundrum.
No UK student has to pay their fees up front - instead, the university is paid directly from the public purse, and the student pays the loan back after graduation.
Scottish students studying in Scotland do not have to pay any fees.
In the other nations, students take out loans to cover their costs; in Wales these are subsidised to a degree by the Welsh Assembly depending on income.