It is felt that presumed consent - the assumption that people support donating their organs after death unless they have previously opted-out - is the most effective way to boost the numbers of organs available for donation.
Even if the presumed consent clause is introduced in Wales alone, any organs retrieved under such a system would be used across the UK and given to the patient representing the best match, it is pointed out.
Organ donation is a non-devolved issue, and although no decision has been made about presumed consent in Wales, Health Minister Edwina Hart has not ruled out seeking a legislative competence order on the issue.
A series of debates are being held around the region to gauge public opinion towards such a system.
In Wales, a record number of people are waiting for a new kidney as the transplant list has once again topped 500 patients.
The Times has reported that the UK government's Organ Donor Taskforce will oppose such a change in its report to be published next week.
Prime Minister Gordon Brown's own backing for presumed consent doesn't seem to have been of any avail.
It quoted a Whitehall source saying: "It's fair to say this report is not helpful to the case for a change in the law to presumed consent."
Roy J Thomas, chairman of the Kidney Wales Foundation and the Donate Wales campaign, said: "It is not a surprise to see that the donor task force in England has rejected the introduction of presumed consent there. We have been aware that the task force has been against a law change for some time.
"Our understanding is that the English task force has advised English politicians about image. The task force has taken into account the image of Whitehall health ministers and not the evidence before it. This is a big moral debate. If government is truly looking at a selfless society, now is the chance. Patients waiting are dying."
Dr Tony Calland, chairman of the medical ethics committee of the British Medical Association, said: "Every year people die because a donor cannot be found to allow their transplant to go ahead. Evidence from other countries has shown that a system of presumed consent can address the shortage of donor organs and can save lives.
"The BMA supports a 'soft' system of presumed consent, where individuals who do not want to donate their organs have a formal mechanism for registering that objection and where families are consulted to identify any unregistered objection. We believe this is more likely than the current system to ensure that the individual's wishes are respected.
"Public support for such a change is already growing but we need to continue to raise awareness and encourage public debate."