A motion listed for debate at next week's England LMCs conference warns that some GPs now 'genuinely feel they can no longer operate within the NHS' because of the crisis driven by rising demand, underfunding and a declining workforce.
The motion will call on the GPC to look at how GPs can operate in a 'private, alternative model'.
But ahead of the LMCs conference, RCGP chair Professor Helen Stokes-Lampard has taken the unusual step of warning doctors' leaders not to support the move.
Read LMC motions in full
'General practice has been the bedrock of the NHS for nearly 70 years and family doctors are doing their utmost to ensure it stays that way, free at the point of need for all of our patients,' she said.
'The current pressures on GPs are immense and we’re going through the toughest of times, but to consider privatisation of general practice in any shape or form is not the answer.'
Dr Stokes-Lampard said that the college understood the 'desperation of GPs' that had led to motions like this being tabled for debate, but warned: 'We must stick together to overcome our current challenges.
'We still believe that NHS England’s GP Forward View is our best chance of securing the future of general practice and that’s why the government in England must make sure its pledges are delivered in full as a matter of urgency.'
