The National Union of Students says it "has concerns" the new scheme might limit the choice of universities available to poorer students.
The no-fee degrees proposal would offer students the option of avoiding the cost of paying tuition fees, which are £3,225 per year from next year.
If fees were to be waived in this way, in exchange students would not be able to claim the package of financial support which can include low-interest loans and means-tested bursaries.
It is anticipated that this might be of interest to the growing number of students who now live at home while studying for degrees.
It might also appeal to students taking higher education courses in further education colleges.
The latest official figures (for 2006-7) suggest 20% of students live at home, up from 8% in 1984.
NUS President, Wes Streeting: "Government needs to be careful"
The director general of the Russell Group of prestigious universities, Wendy Piatt, said there were concerns that such approaches should not reduce the quality of university courses.
The chair-elect of the 1994 Group of research-intensive universities, Paul Wellings, says he welcomes "a diverse range of higher education provision", but emphasises the importance of maintaining quality.
"To ensure quality any new proposals must be fully funded by government - we will be cautious of any new proposals that result in cut-price, lower quality degrees of a lower value to students, particularly in terms of graduate employability," said Prof Wellings.
Wes Streeting, president of the National Union of Students, told the BBC: "I do worry about the future of higher education when those with the ability to pay to study at an institution elsewhere have the traditional experience - the moving away, the gaining of friends and independence.
"Poorer students, on the other hand, could be stuck in the communities they grew up in."
A spokesman for the Department for Business, Innovation and Skills said: "As part of the higher education framework we are considering a number of measures to increase access to higher education and maintain our sector's world class status.
"Ahead of its publication any discussion of the proposals it will contain are purely speculative."
As well as the framework setting out future priorities, the government is to begin a separate review of student fees in the autumn - trying to reconcile the demands for more funding from the universities with the unpopularity of raising tuition fees.
At present, universities are not allowed to raise tuition fees above the fixed cap - and the fees review will have to decide whether this upper limit should be raised or removed altogether.
The proposal for a no-fee degree would provide another option - saving the government the expense of financial support, while allowing students and their families to avoid fees and student debt.
This would depend on students having families that are able and willing to support them.
For parents, it would mean that in financial terms, sending a child to university would be similar to their being in the sixth form at school or college, with the family typically providing accommodation but with no fees for tuition.
There have been warnings that students from poorer families are more debt averse and this could have the appeal of a simple system, with no debts attached.
But it is also likely to raise concerns about inequalities in the student funding system - with different students facing different levels of debts.
There is growing pressure on the university system - and increasingly urgent calls for more funding.
The downturn in the jobs market has sparked a surge of applications for university, with warnings that this is going to create a demand that cannot be met.
Universities have been calling for extra funding to provide more places, but the government faces its own pressures on public spending.
University 'on the cheap'
Member of the UK Youth Parliament, James Greenhalgh, 18, said: "This could be great news for those students who are planning to stay at home anyway, but it is frightening to think how many students would end up choosing a local university, regardless of whether it is the right option for them, because they want to avoid paying tuition fees.
"We shouldn't be trying to tempt students with 'university on the cheap'. They should be able to choose the right course for them, at the right university for them.
"UK Youth Parliament research has shown that a third of young people are already making their university choices based on cost. This figure would rocket if students have 'no fee degrees' waved at them."
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