Brighton health boss Stuart Welling will learn any day now whether he is staying in his post or losing his job.
If he stays as Chief executive of Brighton Health Care NHS Trust, he will work towards improving hospitals in Brighton.
If he goes, the management of the trust could be put out to tender, with bids coming from the private sector or a charity.
Brighton was one of a handful of trusts branded as failing and given no stars in the Government's rating system last September.
The possibility of private sector involvement has met with several opponents, including Brighton Kemp Town MP Des Turner.
He said: "There are times when it can get too bureaucratic and it makes more sense to have a local emphasis.
"I think it would be inappropriate and meet with a great deal of resistance.
"It would have to take a lot of convincing to get me to agree to something like that."
Mike Collinson, chief officer of the health watchdog Brighton, Hove and Lewes Community Health Council, said: "As far as I am concerned, the management we want is the management which will provide the best service possible for the patients.
"With the changes that have been going on in the health service, it is easy to see why the idea of taking over the management of a hospital is a tempting one for some people."
Mr Collinson said he was unhappy with the way the star rating system was established.
He said: "I believe it is flawed. The results are based on figures from several months ago, so a hospital given a zero rating could now be more of a one or a two star.
"It would be unfair if someone loses their job after managing to turn a trust around and ends up being replaced by another organisation, which then takes the credit."
Nurses have also criticised the proposals, saying Mr Milburn has adopted a "pick and mix" approach to running the NHS.
Beverly Malone, general secretary of the Royal College of Nursing (RCN), said: "This announcement is likely to lead to increased bureaucracy rather than streamlining already complex structures.
"The RCN questions whether the private sector has the necessary expertise to run large-scale NHS hospitals, an area in which they have no previous experience.
"With the variety of providers suggested, we need to have guarantees of quality, accountability, transparency and patient involvement.
"We thought we had assurances that nurses providing care to patients in the NHS would remain employed by the NHS. Nurses and patients require some clear answers."
A spokesman for the Patients Association in Sussex said: "This is basically privatisation through the back door and makes me nervous.
"The idea of independent organisations being able to have control over pay structures could lead to all sorts of problems with staff understandably trying to target places which give the most money.
"That type of scenario is not something I would want to see in an organisation that should be concentrating on the patients.
"What is needed is major investment in the NHS so all staff are given a satisfactory wage and patients are given the best treatment."
Mid Sussex district councillor and health campaigner Anne Jones said she was horrified at the idea of the private sector taking over the management of hospitals.
She said: "The South-East has had years of under-funding because it has always been regarded as an affluent area.
"To brand Brighton as failing does not take into account the problems it has to deal with, such as low funding, a large number of residents, a large transient population and a shortage of nursing home beds.
"Bringing in people who have had no experience of the NHS is not the answer."
Hospitals in Sussex say the problems they face are the same around the South-East.
They include a large elderly population that needs regular health care, staff shortages because it is an expensive area to live and a shortage of nursing and care home places.
Brighton says it has done everything it can to improve its performance and says it is not failing.
It says staff are doing an excellent job in difficult circumstances.
David Hinchliffe, chairman of the influential House of Commons health select committee, criticised moves to give private managers "franchises" to take over failing hospitals as "incredibly worrying".
GMB union general secretary John Edmonds also attacked the plans, saying the public did not want to see the NHS become a "new Railtrack".
Mr Milburn insists the proposals are not privatisation in any way, shape or form.
He said queuing was endemic, staff were "run off their feet", there were staff and equipment shortages and patients were disempowered with little choice.
He said: "Healthcare does not need to be delivered exclusively by line-managed NHS organisations.
"A service designed around the needs of patients has to hand over more power to them.
"Who provides the service becomes less important than the service that is provided.
"Just because patients might be treated in a Bupa hospital does not mean they cease to be NHS patients."
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