He cited the number of kidney transplants as evidence of the need for a change.
Dr Richard Simpson, a backbench MSP, wants doctors to be allowed to remove organs unless the patient or relatives object.
That would be a reversal of the current system where a patient's organs cannot be removed for transplant unless specific consent has been given.
Dr Simpson said the donor card system is failing and is considering introducing a members' bill in the Scottish Parliament to move towards a system of "presumed consent".
He cited the number of kidney transplants as evidence of the need for a change.
The number of transplants has dropped over the last 10 years while the number on the waiting list has risen from 4,000 to 6,000.
Dr Simpson said new technology has made it possible to keep an accurate and up to date register of those withholding consent.
He said: "Nobody wants to be putting patients or their relatives under pressure, particularly at times like that which can be very distressing, so we have to build in really very careful safeguards.
Patients' rights
"But I think the advance in the information technology does allow us the possibility of a national register and, if the people of Scotland feel that is something that is appropriate, then the parliament could take it forward through the health and community care committee or through a private members bill."
The idea of presumed consent has long been favoured by the British Medical Association, but it has been opposed by the nursing profession, which said the rights of patients and their relatives could too easily be ignored.
Dangers warning
Margaret Pullin of the Royal College of Nursing said: "Nurses in their whole education and training are taught that there has to be consent of the patients, and it is informed consent.
"Its a huge switch to say we can assume this patient has said we can remove anything we like.
"That is a huge switch and that has dangers attached to it."
Dr Simpson said, with the right safeguards, the new system could increase the number of kidney, liver and heart transplants by at least a third and possibly save hundreds of lives.