KENNET District Council is in negotiations with Wiltshire Primary Care Trust over buying the health clinic site in Devizes and could develop it for car parking.
The council approached the PCT about the Devizes Family Health Centre in New Park Street and has set aside £500,000 to purchase it.
Kennet's director of community services Brad Fleet stressed it was not Kennet's intention to close the clinic.
He said: "We are not negotiating anything that involves a closure. The PCT were approached by the district council and we said if you decide to dispose of the clinic site we would like to be first in the queue.
"We have not signed on the dotted line. We are negotiating to a position but we are not negotiating anything that involves a closure. It's as and when the PCT don't want it."
The flat roofed centre provides clinics for mothers and babies and a NHS dental clinic operates there one day a week.
Mr Fleet said Kennet was interested in buying the site because it was next to its public West Central car park and the new superloo, which cost the council £593,000 to build.
He said the site could be used for coach parking in the future, A spokesman for Wiltshire PCT said: "Under the terms being discussed (with Kennet District Council) health services will continue to operate from the building for five years. During this period services will gradually be transferred to the new health care centre which is planned for the town."
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