The plan, set to be published on 7 April in a report by Tim Leunig, chief economist for the CentreForum think tank, would establish the likely loss to the government of lending money to students at different institutions and on various courses.
Universities would then be asked to make "sealed bids" for places on particular courses and state the tuition fee that they intended to charge. Those considered to represent the "best value" to the Treasury would get the allocation requested.
All places taken up by students borrowing money from the government would be allocated by the system through a process of repeat auctions, while institutions that ended up with excess supply would have to return their spare places so that they could be reallocated.
In the report, Universities Challenged, Dr Leunig says that without the state encouraging genuine competition between universities through such a system, and given the inability of the Office for Fair Access to control prices, institutions would naturally tend to charge the maximum permissible fee.
"If the previous system was simply rolled forward, we would expect almost all institutions to charge the maximum £9,000. They would have every incentive to do so, and no incentive not to do so," he writes.
Times Higher Education understands that the plan is being given careful consideration by ministers at the Department for Business, Innovation and Skills, which is frantically looking for a way to stop universities opening up a predicted £1 billion gap in the public finances by setting their fees too high.
In the past 10 days, another batch of institutions have announced plans to charge fees of £9,000 a year, including the first post-1992 institutions to do so, Liverpool John Moores University and the University of Central Lancashire.
David Willetts, the universities and science minister, has publicly maintained that average fees will be "significantly below" £9,000 thanks to competition from new entrants.
He also has proposed a bidding process for a proportion of places - the so-called "core and margin" model.
But Dr Leunig, a reader in economic history at the London School of Economics, said that most universities would still be able to ignore the competition when setting their fees under such a system.
He said that to drive down prices effectively, the present "command and control" method of allocating places had to be torn up and replaced with one that forced institutions to think more carefully about costs and graduate employability.
In Dr Leunig's plan, data from the Student Loans Company would be used to assess the proportion of borrowed money that would have to be written off by the government on a particular university course, with the figures "standardised" to remove the effect of factors such as gender.
The government would construct a table with its estimates of the costs to the taxpayer, and could then go on to "skew" the results towards students from disadvantaged backgrounds to create an incentive for universities to broaden access.
Dr Leunig, who advocated auctions for public land before they were recently adopted by the coalition government, accepted that the system might be destabilising for the sector in the short term, but argued that the benefits would make it worthwhile in the long run.
Asked if universities might also become too focused on training graduates for jobs, he said: "That is a risk, but students are much more job-focused now so for universities to move a bit more in that direction is no bad thing."