Would bringing universities back under the control of the Department for Education improve social mobility by restoring the policy link between schools and universities? Or would it be a case of "rearranging deckchairs" as the economy struggles, and expose universities to the "interventionist" policies of Michael Gove?
Senior sector figures have given conflicting views amid growing speculation that Mr Gove, the education secretary, is pitching for the government to make such a move before the next general election in 2015, with the aim of creating a policy synergy between schools and universities, especially on fair access.
The position of universities in Whitehall has been pushed to the fore in the political battle over the appointment of Les Ebdon, the vice-chancellor of the University of Bedfordshire, as the next director of the Office for Fair Access.
The conflict over Professor Ebdon's appointment is seen as part of a wider attempted "putsch" by Mr Gove to undermine the Department for Business, Innovation and Skills, currently responsible for higher education, while it has also exposed divides within the coalition and, arguably, the Conservative Party.
Mr Gove's chance of success in wresting back control of higher education funding is increased by his powerful political position. He is already a key player in the inner circle of Conservative power in the Cabinet and is seen by some as a potential future prime minister.
David Ruffley, a Tory member of the Treasury Committee, this week called for BIS to be abolished. "We should redistribute...higher education and science back to the Department for Education, where Michael Gove wishes it to be," he said.
Holding sway over all aspects of education policy would enable Mr Gove to drive forward some of his reforms, including tackling declining confidence in A levels by involving the academy more in the process of setting exams and inviting universities to run free schools.
Alan Smithers, director of the Centre for Education and Employment Research at the University of Buckingham, said this would be one concrete benefit of bringing the briefs together. "Our A-level examinations have got a bit out of touch with higher education. We need a minister in there to ensure that the universities are fully involved," he said.
Professor Smithers said restoring the policy link between secondary education and universities would also do much more for social mobility than Professor Ebdon's appointment.
Some critics of the present arrangements believe that the previous government's motivation for "chopping and changing" the departmental location of higher education was suspect: they suggest that BIS was created in 2009 to give Lord Mandelson a large brief on his becoming First Secretary of State.
"Most other countries manage perfectly well with a ministry of education (with or without science attached). We should follow their example," said Sir Peter Scott, professor of higher education studies at the Institute of Education, University of London.
Those in favour of retaining the status quo argue that one of the key reasons why universities and further education colleges were moved closer to industry and science policy in the first place is that they help to drive growth.
"While the economy is in desperate straits, to be seen to be mucking about with the deckchairs - and specifically with the deckchair that is higher education within the growth department - would be odd," said Andy Westwood, chief executive of GuildHE and an adviser to John Denham when he was universities secretary in the Labour government.
Mr Westwood said a major departmental reshuffle would be extremely difficult without a "recasting" of the coalition agreement between the Liberal Democrats and the Tories, making a move before the next election unlikely. Key to this is the fact that without higher education, Vince Cable, the business secretary, would be left with a tiny department.
Bahram Bekhradnia, director of the Higher Education Policy Institute, also said that although in the "purest sense" one department covering all levels of education might be appealing, it would be "practically and politically" difficult to achieve at present.
"One worry is that the rather interventionist policies that secretaries of state for education - and particularly this one - seem to favour for schools would be not appropriate for higher education," he added.
Better out than in, v-cs thought when supersized department was mooted
A crucial factor in any consideration of whether to shift responsibility for higher education to Michael Gove and the Department for Education will be financial: not only in terms of the huge cost of reorganising the departments, but also the resulting size of their budgets.
Before the last general election, senior vice-chancellors in the sector held meetings with Whitehall officials about the ramifications of making the move, which was considered in the aftermath of the poll.
The vice-chancellors argued strongly for the status quo on political and financial grounds. By keeping higher education in the Department for Business, Innovation and Skills - where, along with science, it accounts for about two-thirds of the department's budget - they felt it would suffer less in the government's 2012 Spending Review.
One key reason was that although universities had historically benefited from an "under-spend" by schools in the education department, the fear was that the opposite could happen when spending was cut, and higher education would be squeezed.
Some experts are sceptical of this line of argument. Roger Brown, professor of higher education policy at Liverpool Hope University, said the fact that university funding comprises such a large percentage of BIS' total expenditure leaves institutions more vulnerable.
"Higher education has suffered from being in BIS. If it were in Education, any cuts across the board would be easier to handle, as universities would make a smaller proportion of the department," he said.
However, he added that higher education had always been a "silo" in government and that its position was "far less important than who the minister is at the time and what policies they are pursuing".
Andy Westwood, who worked as an adviser in the Department for Innovation, Universities and Skills - the first Labour incarnation of higher education outside the education department - said the history of its position in Whitehall was also more complex than imagined.
DIUS was created in 2007, after Gordon Brown took over from Tony Blair as prime minister, in an effort to bring science and university funding together. When a new ministry was created for Lord Mandelson in 2009, DIUS was merged with the business department.
Mr Westwood said that before 2007, when responsibility for higher education lay with the Department for Education and Skills, research council funding was still in the Department for Trade and Industry.
"So there was an admission even then that the science and research budget was part of that innovation and growth strategy, and if that was true then, it must be true now," he said.
One option would be to bring both science policy and higher education back into the Department for Education - which was the case from 1964 to 1992 - but this would make the department one of the biggest in government, especially if further education were also included.
Such a move would need to be weighed against the sheer cost of reorganising in an era of austerity. Figures published in 2009 suggested that it cost the Labour government £9 million to set up DIUS.
Where the money is: departmental budgets 2011-12
Department for Education
Total resource and capital budget: £56.3 billion
Schools: £43.2 billion
Education for 16- to 19-year-olds (including sixth forms): £8 billion
Department for Business, Innovation and Skills
Total resource and capital budget: £17.7 billion
Higher education (excluding student loans): £6.6 billion
Science and research: £5.3 billion
Skills and further education: £4.1 billion
Potential size of "super" education department, including science and further education: £72.3 billion.