The centre in Sidwell Street s the subject of a review which also includes out-of hours services and minor injuries units.
Campaigners are preparing to present a petition to the local Clinical Commissioning Group next week.
There's a proposal for Exeter to have one or more urgent care centres providing these services, and various organisations are bidding for the contract.
Deaths of man and woman in two counties being linked
Woman found dead in Torquay; man in Hampshire
Dawlish's black swan lose nests in floods
At least 10 eggs washed away
Trains cancelled as flood damage continues
Divers to inspect infrastructure
Torbay tourism facing pressures
Bay MP says tourist trade needs stability and help
What is the future of vulnerable but vital Slapton Line?
Millions of pounds have already been spent protecting the road
