Many believe putting a price tag on face-to-face consultations is the only way to manage the increasing workload and rising patient demand, health magazine Pulse said.
In a poll of 440 GPs by the magazine, 51% said they would support imposing a small fee to visit a GP, compared with 36% who would not.
Last year a similar poll found only a third of GPs would support the move, suggesting a growing number are willing to consider drastic solutions to reduce their workload.
Demand for routine appointments is likely to double in the next two decades, according to a report published last year by the Deloitte Centre for Health Solutions.
The majority of GPs who called for charging specified an amount between £5 and £25 per appointment, Pulse said.
One suggested means-testing how much patients pay for visits, charging the "poor" £10, professionals and politicians £100 and solicitors and accountants £150.
Stephen McMinn, a GP in Bangor, Northern Ireland, said the introduction of a fee could help to reduce the demand for appointments.
But other GPs argued the move could end up costing the NHS.
Edmond Ferdinandus, a GP in Wakefield, West Yorkshire, said: "A small fee will make patients feel they have a large entitlement - if we do this, I predict the extra income will be entirely cancelled out by extra prescriptions, investigations or referrals."
Chaand Nagpaul, chairman of the General Practitioners Committee which represents GPs in Britain, said the NHS should be free at point of delivery.
"Charging patients would have adverse effects and would fundamentally be to the detriment of GP-patient relationships. We need to preserve trust between patients and their GPs," he said.