Eric Thomas, vice-chancellor of the University of Bristol, highlighted the scheme to David Willetts, the universities and science minister, in an email in March 2011, before he became head of UUK.
The email, obtained by a Freedom of Information request, was published on the website whatdotheyknow.com and reported by the Bristol student newspaper Epigram.
Under the scheme, a student would sign a contract with a special purpose company, acting for a university or group of universities, to repay a fixed percentage of their earnings over a set number of years. Banks would package the graduate contracts and sell them on to investors, particularly pension funds.
"The sale proceeds will vary based on the market's perception of the future earnings potential of the group of students," according to a 2010 explanatory document by Peter Ainsworth, managing director of EM Applications, a firm that advises investment managers.
The system - known as Fair, which stands for funding with affordable income-based repayments - envisaged uncapped, variable fees.
Mr Ainsworth was asked by the Russell Group to write up his ideas in the document, although he did not receive any funding.
On 25 March 2011, Professor Thomas, who became president of UUK in August of the same year, wrote to Mr Willetts that discussions around the private financing of student support "may be more acceptable now than previously".
"I have seen Peter Ainsworth recently about the FAIR proposal which your office has seen. If you would like to reconsider how this may be taken forward again, I am happy to discuss informally," he wrote.
Speaking to Times Higher Education, he said: "I did not endorse the Fair proposals. I drew the proposals to the minister's attention but did not endorse the proposals."
In a reply on 19 April 2011, Mr Willetts thanks Professor Thomas for sharing the proposals but writes that "it is less attractive than the approach we have adopted".
Specifically, the Fair system would not be available to students older than 23 and would levy a charge on all levels of income, rather than above a salary threshold as is currently the case, Mr Willetts writes.
The Fair document says that if "future earnings of [universities'] students did not justify their average cost per student [universities] would need to find strategies to raise those future earnings or reduce their costs".
A University and College Union spokesman said degrees should not be targeted "solely at those students likely to return the best investment".