Two former cabinet ministers have raised concerns about the proposed appointment of Australian Carol Mills as Parliament's senior official.
Former foreign secretaries Jack Straw and Margaret Beckett have added their voices to a cross-party campaign for Ms Mills to face a confirmation hearing in front of MPs before she can take up the role.
Ms Mills, head of the Department of Parliamentary Services of the Australian Senate in Canberra, is believed to have been recommended for the prestigious role following a recruitment process with a selection panel led by Speaker John Bercow.
But concerns have been raised about her ability to fulfil the role as adviser on parliamentary procedure and constitutional matters, with former speaker Baroness Boothroyd claiming she would be "totally out of her depth".
Public Administration Committee chairman Bernard Jenkin has written to David Cameron asking him to back a pre-appointment hearing with Ms Mills, a move backed by Mr Straw and Mrs Beckett .
Mr Straw, a former leader of the Commons, told The Guardian: " Given the controversy, and without making any observations about the relative merits of the candidate, I think that such pre-appointment scrutiny would be a good way of resolving this."
Mrs Beckett, who also served as leader of the Commons, told the newspaper: "These days you cannot make an appointment like this without select committee scrutiny."
The £200,000-a-year position combines the role of clerk of the House of Commons and chief executive responsible for running the building and managing almost 2,000 staff.
Critics have said that while Ms Mills' may be a suitable candidate for the chief executive element of the job, they are concerned about her ability to advise MPs, the Speaker and Prime Minister on constitutional matters.
Mrs Beckett said: " The idea of having a chief executive role, which is not the clerk to the House, has often been discussed in the past.
"But as far as I know the house has never decided actually to go down that road. It is a step of perhaps major constitutional significance as far as the house as a whole is concerned."
Mr Bercow - who has attempted to drive a significant modernisation of the Commons - has come under fire for overlooking the respected deputy clerk David Natzler for reasons of political correctness.
But his allies have defended the way it was handled, with an open recruitment process and lengthy interviews for the shortlisted candidates.
Mr Bercow chaired the appointment panel which also included Andrew Lansley - who subsequently lost his job as Commons leader in the reshuffle - shadow leader Angela Eagle, Labour chairwoman of the Public Accounts Committee Margaret Hodge and Liberal Democrat John Thurso.
Parliamentary and Health Service Ombudsman Dame Julie Mellor was the external panel member.
Mr Bercow's spokeswoman said: "This is the first time ever there has been an open and fair recruitment process for the clerk of the House of Commons."
Eight candidates were interviewed, with a shortlist of three called back for a second round of grilling by the panel.
The Speaker's spokeswoman said the candidates were "scrutinised very carefully indeed"
The successful candidate's name is understood to have been put forward to Downing Street to subsequently recommend to the Queen.
The vacancy has arisen because of the retirement of Commons veteran Sir Robert Rogers amid claims he has clashed with the Speaker.
Tory MP Michael Fabricant, who claimed in the Commons last month that Mr Bercow had once told Sir Robert to "f*** off" in front of witnesses - an allegation immediately denied by Mr Bercow - said the Speaker should consider resigning.
On Twitter he said: " If I were #Bercow, I'd be thinking about my own position, let alone considering what to do about the rigged appointment of the new Clerk."
Sir Robert has put in place a plan for when he retires at the end of the month, with Mr Natzler acting up as clerk until the new appointment is in place and Dame Janet Gaymer chairing the Commons management board.
The outgoing clerk told BBC2's Newsnight: "I have put interim arrangements in place. Dame Janet Gaymer will chair the management board, and the clerk assistant will act as the clerk in the House."
Sir Robert indicated that the arrangement could remain in place for months if wrangling over his replacement continued.
He said the plans "are resilient" and that "we could go to the election without a problem. I'm quite sure we would be fine".