Politicians have been meeting with health officials in the latest attempt to safeguard the future of services at Corby's Urgent Care Centre.
Lakeside Plus, which runs the service, had threatened legal action against the NHS over a new contract for operating it - but that has now been dropped.
However, they say that they can no longer afford to keep running the centre and may have to reduce services later this year.
On Monday, the leader of Corby Borough Council, Tom Beattie, met with the NHS Corby Clinical Commissioning Group (CCG); while the MPs representing Corby, Kettering and Wellingborough met with Lakeside Plus.
"We are very willing to have conversations with the CCG about continuing to deliver the service," Lorna Garner from Lakeside Plus told the BBC.
"The CCG have no intention of closing the centre. [But] it's the level of service they [patients] get, it's the quality of clinical care that is delivered [that must be safeguarded]. That is our main concern - that that standard is continued.
"The building is irrelevant, it's what happens inside it that really matters."
An independent expert is expected to rule early next month as to how much it should cost to run the centre.
The CCG has declined to comment until that ruling is made.
Tom Pursglove, Conservative MP for Corby, said: "If there's absolutely no chance whatsoever of this service closing, then they [the CCG] need to say that.
"This is a case of keeping full scale pressure on this. We simply can't get into a situation where this service is lost - it would be wholly unacceptable."