The report from the Commons select committee that has been investigating the work of the Office for Standards in Education is expected to recommend that the embattled chief inspector be supervised by a ministerially-appointed board.
Among the concerns of MPs who have spent months examining evidence submitted by academics and teacher unions are the personal style of Mr Woodhead and the unparalleled independence given to chief inspectors when OFSTED was created.
The all-party group of MPs is expected to suggest that the school inspection service's unique status as a Government department without a minister is not sufficiently accountable to the public.
The solution, the report is likely to suggest, might be the creation of a board, bringing OFSTED in line with the quangos that advise the Government on the school curriculum and teacher training.
However, the suggestion that Mr Woodhead's personal style may also be part of the problem is likely to be politically embarrassing in the wake of the prominence that has been given to revelations about his relationship with a former sixth-former at the school where he was head of English.
MPs are likely to say that Mr Woodhead has not gone out of his way to encourage a positive response from teachers.
Ministers are keen not to get embroiled in further controversy about Mr Woodhead, but they are also reluctant to impose restrictions on him. In her evidence to the committee, Estelle Morris, the standards minister, rejected changes to OFSTED's structure.
She told MPs: "I don't think there is much wrong with the way we are doing it at the moment. If I was worried about accountability, it might be worth looking at more bureaucracy, but I would have to be persuaded there was something wrong with the present system."
The report is likely to separate the role and status of the chief inspector from the system of school inspection. In the main, MPs on the select committee have been impressed by the inspection regime and they believe most schools value an OFSTED review. In particular, they cite the OFSTED framework, which sets out the basis for judging schools, as having had an impact.
In his evidence, Mr Woodhead suggested he was directly accountable to Parliament through the education select committee. However, MPs believe that the present structure does not allow enough day-to-day scrutiny of OFSTED.