Scottish universities have indicated for the first time the level of tuition charges they think could be introduced.
Universities Scotland said unless future graduates paid up to £13,000 for their four-year degrees the number of student places would be unsustainable.
The comments came in a leaked response to the Scottish government's green paper on higher education.
Universities Scotland said a graduate contribution could be set at the current English level of £3,290 a year.
However, the report said graduates who earned a "relatively low" salary should not pay.
Tuition fees were abolished in Scotland in 2000, two years after their introduction by the Blair government at Westminster.
A one-off graduate endowment fee of just over £2,000 was scrapped by Scottish ministers three years ago.
However, there is increasing pressure to find a new method of funding for Scottish universities, especially after tuition fees in England increase next year.
Universities Scotland, which represents university principals, said in its report that the extra funding made available to universities in England through rising tuition fees and an increased flow of government loans to students would leave them better resourced than those in Scotland.
Funding for Scotland's university sector will reduce by £67m in the year ahead, as part of a cut of about £1bn in the 2011-12 Scottish budget.
The report said Scottish universities were already preparing to lose hundreds of posts and cut courses as a result of the funding gap.
Student places, it said, would be maintained in 2011-12, despite an 11% cut to the Scottish Funding Council's teaching budget.
But Universities Scotland said this could only happen for one year "at a severe stretch".
It said in future the state should retain the prime responsibility for university funding.
However the report added that it was fair to expect graduates "who realise substantial private benefit as a result of a university education" to bear some of the financial burden.
The report said: "Provided public funding for universities is not cut further, a Scottish graduate contribution could be set at a level which is much closer (or lower than) the former English level of deferred contribution, than to the highly contentious model which is now being implemented in England."
Students at English universities currently pay £3,290 a year but this could rise to as high as £9,000 at some institutions when new rules come into force.
After the proposals were published, Liam Burns, president of the National Union of Students in Scotland, said: "To attempt to bounce people into tuition fees in Scotland by needlessly alarming prospective students is reckless and playing politics with people's futures.
"Tuition fees are unfair and have been entirely discredited. We've seen how divisive they can be in the rest of the UK and we must avoid anything like the same approach in Scotland."
Education Secretary Michael Russell said: "The joint work we are currently engaged in with Scotland's universities will lay out the scale of any gap in funding that might open up in future years, and will report early in March.
"The debate is not about whether we need a funding solution that ensures our world class universities remain competitive, it's about how we achieve this."
Scottish Labour's Des McNulty said the paper showed the extent of the "impending crisis" facing higher education in Scotland.
"In the face of massive cuts in the teaching grant south of the border, which will have implications for Scotland, and the huge hike in tuition fees imposed by the Conservative-led government, all the SNP have come up with so far is a green paper," he said.
"It has failed in its responsibilities as the party of government to come up with proposals for sustainable future funding arrangements."
Liz Smith, the Scottish Conservatives' education spokeswoman, said: "Universities Scotland is rightly concerned about the future funding of universities and I welcome their support for our policy of introducing a graduate contribution.
"The situation which Scottish universities face is grave and unless there is immediate action to invest more in the sector then we will not only see fewer places for prospective students, but a diminution in quality and standards with our universities falling behind those in the rest of the UK and internationally."
Liberal Democrat education spokesperson Margaret Smith MSP said: "What's come out today still doesn't answer the essential question of what the funding gap is between Scotland and England and what the impact is in terms of competitiveness.
"We need a long term solution to higher education funding in Scotland."
A working group involving Universities Scotland will report to a cross party summit on 1 March.