The Handa Practice, an offshoot of the Condorrat Medical Practice, has this week launched a consultation exercise about closing the service down.
The consultation, which started on Monday is set to run until the end of the month and is looking to gather views and feedback via a patient questionnaire.
Once these have been collated a final decision will be taken on the future of the village practice.
The News spoke with practice manager Allison Flaherty who advised that they would be making no comment until such time as their decision was known at the completion of the consultation, but did say there were a number of reasons behind the exercise.
The proposed date for closure would be March 31 at which point patients would transfer to the main practice in Condorrat.
Central Scotland and Scottish Conservative MSP Margaret Mitchell announced last week that Lanarkshire has lost 11 GP practices since 2008.
Recent warnings from the Royal College of General Practitioners say that Scotland could be short of more than 800 family doctors by 2021.
Cllr Gillian Fannan said: The Handa Practice is a much needed service, especially for elderly patients who find it difficult to travel. Its closure would be a huge loss.
“People in Cumbernauld have suffered from under investment in their health services, and this is just the latest in a long line of closures.
“I would urge everyone to take part in the patient consultation, which ends on the January 31. You can pick up a questionnaire in both the Village or Condorrat practices.”