The Nuffield Orthopaedic Centre has been given the go-ahead to bid for foundation status.
But the Oxford hospital must retain its three-star grade, if it is to be successful.
Foundation hospitals will be controlled by a board made up of community members, and will be free from some Government control.
Although the status will not bring extra money, foundation hospitals will be allowed to borrow funds from the private sector to increase their annual budget.
Health Secretary Alan Milburn announced the shortlist of 29 UK hospitals on 14 May.
The NOC, in Headington, must now consult the public before applying for foundation status by the autumn.
As part of the bid, managers will have to show how they plan to help other hospitals in the area improve, and how foundation status will enable them to upgrade patient services.
To keep the hospital's three-star status, managers must also keep waiting times and cancelled operations down, and stay on budget.
NOC chief executive Ed Macalister-Smith said the trust would consider the views of staff, patients, carers and other health organisations before applying for foundation status.
He said developments would be made to improve patient services, borrow money for improvements and change the way the trust was administered and controlled.
Thames Valley Health Authority, which oversees health services in Oxfordshire, Berkshire, and Buckinghamshire, has given its full support to the NOC -- the only hospital to win foundation status in the area.
The authority's chief executive, Nick Relph, said: "It's good news for the NOC, which has an excellent reputation for the quality of care it provides for local people."
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