A report by The Fraser of Allander Institute at the University of Strathclyde has recommended that the next Scottish Government should charge for those willing to take extra places on Scottish degree courses.
The Fraser of Allander Institute report also suggested that Scots should pay a graduate contribution after leaving their institution.
Currently, the Scottish government decides how many Scots students can be enrolled in universities and pays for those places, and the Scottish Conservatives are the only political party not to rule out the policy of charging tuition fees.
The report says, as an example, that a law department with enough staff and space in lecture theatres to take 80 students would be able to take in 10 fee-paying students over and above the 70 places paid for by the government.
The report's author, Professor Jim Love, suggested private fees in line with government fees, currently between £4,000 and £16,000 a year.
The report said: "Governments could restrict themselves to being in a contract with universities to purchase given numbers of student places.
"Equally, of course, universities, as autonomous institutions, should be able to decide whether they wish to take student numbers and fee levels as offered by government.
"Removal of control numbers and the associated clawback arrangements would allow universities to offer places on programmes to home or EU students currently denied access, provided they satisfy entry requirements."
Edinburgh Napier University declined to comment on the issue, on the grounds that it “had not entered the tuition fee debate.”
Universities Scotland director Alastair Sim said: "There are some interesting ideas in the Fraser of Allander paper.
"But as four of the five main parties have now ruled out contributions of any kind from students or graduates, the focus now needs to be on Scotland's politicians stepping up to the mark to find the public funding necessary to keep our Scottish universities competitive with those in England."
He added: "Our greatest concern about another review of Scotland's universities is that it cannot be allowed to delay the urgent need to plug the funding gap that will start to emerge between Scotland and England's universities from next year. Preventing that from happening will need immediate action after the election."