The Scottish government is seeking views on recommendations by an independent expert panel to introduce a "no-fault" scheme in Scotland.
The group has recommended changing the current system for the handling of claims to one of no-fault compensation.
The system would be similar to schemes in place in other parts of the world.
A change would mean patients who have suffered loss, injury or damage as a result of treatment could be compensated without going to court to prove negligence.
The No-Fault Compensation Review Group, headed by law and medical ethics expert Professor Sheila McLean, was set up in 2009 by the health secretary.
The proposed new system would still require proof that harm was caused by treatment but would remove the need to prove negligence.
Minister for Public Health Michael Matheson said: "We know that the vast majority of the care delivered in our NHS is of the highest quality, but it is important that people who have suffered as a result of clinical mistakes should have some form of redress.
"It's in no-one's best interests to have that redress delayed because a compensation claim can take years to go through the courts.
"Nor is it in anyone's interests to have precious NHS resources spent on expensive legal fees."
He added: "It is important that we seek wider views in order to help in our understanding of what the practical implications would be."
No-fault systems are already in place in countries such as Sweden, Norway, Finland, Denmark and New Zealand, and parts of the US.
Welcoming the move, the BMA said the system should speed up the process, but cautioned that it should not increase costs to the NHS and take money away from patient care.
A consultation has begun on whether the NHS should compensate people when things go wrong without victims having to go to court.