Lord Sutherland was also formerly principal of Edinburgh University
Tuition fees should be reintroduced in Scotland, the former head of Universities Scotland has said.
Lord Sutherland said some of the money should go to scholarships to pay for students from poor backgrounds who cannot afford fees and living costs.
Up-front tuition fees were abolished in Scotland in 2000, two years after their introduction by the Blair government.
A student union said tuition fees were rejected by consensus and top-up fees in England had not increased access.
Tuition fees were introduced in 1998, by Tony Blair's Labour government.
However, in 2000, the Labour and Lib Dem coalition in Scotland abolished up-front fees north of the border, following the Cubie inquiry into student finance.
While top-up fees of up to £3,000 were introduced in England and Wales in 2006, the following year the SNP administration abolished the fees altogether.
However, according to the latest statistics from Higher Education Statistics Agency, Scotland had fewer university students from disadvantaged backgrounds than any other part of the UK.
A total of 26% of students in Scotland come from poorer backgrounds, compared with 40% in Northern Ireland and 30% across the UK as a whole.
Lord Sutherland, who was also formerly a principal of Edinburgh University, told BBC Scotland: "People who are intellectually talented come from all corners of society and they're the ones who should be going to university, and we should help.
"I think offering scholarships is very important because the cost of going to university - fees and living costs - are high.
"One way of doing this would be to make sure that those who can afford it do pay tuition fees and ensure that a percentage of that goes to the scholarship for those who can't afford it."
BBC Scotland's education correspondent Seonag MacKinnon said a lot of senior university figures privately believe the current situation advantages middle-class students who dominate Scottish universities.
She said the public purse in Scotland had so far matched what has gone into universities south of the border from top-up fees.
But the correspondent added that public spending cuts were expected in Scotland and there was a feeling that funding at that level was not sustainable, given the widespread expectation that fees south of the border were set to rise to about £5,000 after the General Election.
However, Liam Burns, from the National Union of Students in Scotland, said when fees were in place in Scotland, a consensus had been reached that parliament and universities did not want the system.
And Tony Axon, spokesman for the University and College Union Scotland, said. "No political party or any current head of a university is calling for such fees.
"His attempt to legitimise the reintroduction of fees by calling for increased bursaries for students from poorer backgrounds reveals that he has clearly not properly investigated the failing system south of the border."
A spokesman for the Scottish Government said: "We believe that access to education should be based on the ability to learn, not the ability to pay and have made clear that we are opposed to tuition fees in Scotland.
"The Scottish Government has restored the principal of free education in Scotland, abolishing the graduate endowment fee benefitting up to 50,000 students and graduates."