A cull of quangos is being planned, raising speculation that the Higher Education Funding Council for England could be among those in the line of fire.
Liam Byrne, the Chief Secretary to the Treasury, has asked Whitehall departments to review all their quangos with a view to possible merger or abolition.
The Conservative leader, David Cameron, also pledged this week to cut the number of quangos - and their executives' pay - if he comes to power.
Andrew Haldenby, director of the think-tank Reform, said that responsibility for how much money universities should be given was a "fundamentally political question".
Writing on 6 July, he argued that Hefce "should be taken back in-house, into a government department, so that ministers are fully accountable for its decisions".
However, David Willetts, the Tory Shadow Universities Secretary, said it was not Conservative policy to scrap Hefce, which had a "constitutionally essential role" in standing between ministers and universities.
The Liberal Democrats have indicated that they would replace Hefce and the Learning and Skills Council with a single Council for Adult Skills and Higher Education.
With Hefce's future under scrutiny, others have leapt to its defence.
Bahram Bekhradnia, director of the Higher Education Policy Institute, said scrapping it would save little money and would create a "major governance issue".
He said: "This would go against a worldwide trend for governments to try to create distances between themselves and universities. Personally, I would see Hefce's abolition as a very serious and retrograde step."
Anna Fazackerley, head of education at the think-tank Policy Exchange, said she was "unconvinced" that scrapping Hefce would be a good idea. "Should a government department be concentrating its efforts on calculating funding formulae for teaching different subjects? I don't think so," she said.
However, she suggested that other sector bodies were ripe for the plucking. "Top of my list would be the Quality Assurance Agency, which seems to monitor paper trails and not quality," she said.
Terence Kealey, vice-chancellor of the private University of Buckingham, said that "as quangos go, Hefce is among the best". He said: "It genuinely tries to provide money to universities according to academic and objective criteria, and the idea that it should be replaced by direct funding ... and so render universities even more vulnerable to governmental direction is appalling."