In a letter leaked to the BBC programme Here and Now the Student Loan Working Group - made up of representatives from the Treasury, the Bank of England and the Department for Education - outlines its two options.
It suggests the Treasury might give private banks and credit companies hundreds of millions of pounds in subsidies to take over the loans under the current interest-free repayment system. The other suggestion is for banks to take over the running of the service, with commercial interest rates to be charged once repayment began.
Problems with the current arrangement were highlighted this week when Government figures showed that repayments of loans last year by graduates amounted to just Pounds 19.8m, compared with Pounds 751m still outstanding.
Some 20 per cent had been allowed to defer repayments because of low income.