Sir Martin Harris is to stay on as director of fair access for another four months after the government failed to find a suitable candidate from outside the sector to replace him, Times Higher Education has learned.
Following interviews for the job that started in October, ministers were left with just one name - understood to be David Allen, registrar and deputy chief executive of the University of Exeter.
Under public appointment rules, ministers should ideally be presented with at least two candidates. Liberal Democrats in the coalition are also keen for the new director to be from outside higher education - possibly from the schools sector - to ensure the independence of the post.
Although Mr Allen has not been rejected, his name will be carried forward as ministers extend the search into next year in the bid to attract more candidates.
Sir Martin - who temporarily stepped down from the role in the summer to receive treatment for cancer - will stay in the post until the end of April 2012, when the process of setting tuition fees for the academic year 2013-14 will be well under way.
It creates yet more uncertainty for higher education as it awaits the government's official response to its White Paper consultation, including whether it plans to grant Offa more powers to penalise universities seen as failing on access.
The quango was at the centre of the row over tuition-fee levels, with some ministers - including the deputy prime minister Nick Clegg - wrongly assuming that Offa had the power to force universities to lower charges.
Lib Dems would like to see more legal powers for the body, but they also view the appointment of a new director as a crucial chance to give Offa more political clout.
Andy Westwood, chief executive of GuildHE and a former ministerial special adviser, said the delay was "not helpful" given the government's timetable for reforms. But he added that the appointment was "slap bang in the middle of coalition politics".
He said that while the Lib Dem instinct was to make Offa a "very tough regulatory agency", some Tories - including David Willetts, the universities and science minister - were "happier" for it to have a more "consensual" approach.
"Other than teaching funding, this is the most powerful player that ministers can have a hand in the appointment of," Mr Westwood said. "It is a bit like appointing someone to the US Supreme Court. You get a chance to appoint in your own image, and that is quite hard when you have some differences in view between the two parties in the coalition."
Mr Westwood said that finding someone from outside the sector might be a "big ask", given the political tensions, the technical detail of access issues and the limit on salary.
"I dare say they are under some pressure not to pay more than the prime minister's [salary]," he said.
In pursuing the top post at Offa, Mr Allen's background in higher education may not be the only factor working against him.
Exeter is among the bottom 10 universities in England on three main widening participation indicators - those with the fewest students from state schools, from less wealthy socio-economic classes and from low-participation neighbourhoods.
A spokeswoman for the Department for Business, Innovation and Skills said: "This is an important public appointment so the government is seeking a wide range of candidates from across the higher education sector and beyond.
"Ministers have decided to extend the application process on the advice of recruitment experts. Any appointable candidates from the earlier applications round will be carried forward."
The job search is being overseen by an "independent assessor" from the Office of the Commissioner for Public Appointments.
Its official guidance states that ministers should be given a selection of at least two "appointable" candidates after interviews - although it is possible for only one name to be put forward.
In a separate development, it has emerged that the government has boosted Offa's budget this year, up from £484,000 to £630,000, to help deal with the increased pressures of the new regime.
However, this is still well short of the increase of up to four times in capacity that the government's White Paper says it may ultimately provide for the body.