OXBRIDGE colleges are unlikely to hold on to the full college fee, worth a total Pounds 35 million a year, once a government review is completed this autumn.
But they are confident they will be able to keep enough of the money to maintain the college fees system, perhaps on condition they can prove they earn it.
The Higher Education Funding Council for England will decide its position on the issue next week.
All is still to play for until that meeting, when board members may decide to present ministers with a number of options rather than a clear decision.
The funding council has been looking for proof from Oxford and Cambridge that they deserve extra money because their quality of teaching and their costs are higher than at other universities.
Brian Fender, HEFCE chief executive, said Oxford and Cambridge already do well out of the block grant.
College heads say they have presented clear evidence that they provide special quality, but many are expecting more pressure to improve access for state school pupils.
Education ministers are known to be unhappy with the idea that Oxbridge should have more privileges than universities with more poorer students.
Margaret Hodge, a member of the education and employment select committee, who met Oxbridge students last week, said extra money for colleges was an anomaly.
"We are trying to work with a lot of universities and further education colleges that have run out of money. The onus is on Oxbridge to find ways of revising their ways of working," she said.