The Cambridgeshire hospital's debts of £40m have been underwritten
A failing hospital looks set to become the first of its kind to be run by a private firm, after the only NHS bidder withdrew from the race to manage it.
Five private health providers are still vying to manage Hinchingbrooke district general in Cambridgeshire.
A boss from the East of England health authority denied the move amounted to the privatisation of the service.
But a health union warned the hospital was part of a "dangerous experiment" involving bidders with no experience.
The health authority's director of strategy, Stephen Dunn, said all the companies in the contest had provided elective surgery, such as knee and hip replacements, to NHS patients in treatment centres.
He said: "The NHS remains firmly part of this process. Staff and assets will remain in the NHS. They are not being sold.
"This is not about selling the family silver. This is not about privatisation. These worries are just unfounded."
But a spokeswoman for health union Unison said it was a waste of public money to go through a process of "market testing" just as Hinchingbrooke started making progress.
She said she was worried most private sector companies did not know how to run a hospital with intensive care, maternity and emergency services.
"The experience in the UK is that when you have an emergency in a private sector hospital it is transferred to the NHS. This is a dangerous experiment," she said.
Earlier this week Cambridge University Hospitals Trust withdrew from the race to run the large, debt-ridden hospital in Huntingdon from April 2011.
A spokesman for the Trust said: "The competitive bidding process will involve considerable investment in both time and money.
"Continuing to take part would have an impact on services at Addenbrooke's and The Rosie. Accordingly, we have decided to withdraw from the project."
Any incoming company would have to help repay an NHS loan being used to underwrite the hospital's £40m debt.