Health Secretary Alan Johnson has asked advisers to look at whether everyone in England should be put on the organ donor register unless they opt out.
There is a major shortage of organs available
The move has been recommended by England's chief medical officer to tackle the chronic shortage of organs.
But the proposal to force people to opt out of the system, as opposed to voluntarily opting in, is contentious.
"This is a sensitive issue," Mr Johnson said, but he stressed it was "vital" all possible options were explored.
There are currently more than 8,000 people in the UK who need an organ donation but only 3,000 transplants are carried out each year. It is estimated that one person dies each day waiting for an organ.
Only 24% of the population - or 14.6 million - are on the register, despite the fact that in surveys as many as 90% of people say they want to donate their organs after death.
Because so many people die in a manner which makes them unsuitable donors, the pool of potential donors must be substantially larger than the numbers waiting for organs.
But a system of presumed consent, as recently recommended by Chief Medical Officer Liam Donaldson, was rejected by MPs when they voted on the Human Tissues Act in 2004.
Any change to the system of consent would again have to be put to parliament.
Scotland's Chief Medical Officer Harry Burns in July rejected the idea for Scotland, saying there was no evidence that the public would support such a move.
The Organ Donation Taskforce was established by the government in 2006, charged with "identifying barriers to organ donation".
It comprises 20 experts including transplant surgeons, anaesthetists, transplant co-ordinators and NHS managers.
It will examine all the issues surrounding presumed consent, including the practical, legal and ethical.
It is highly likely to look at the successes of such schemes abroad.
Several countries, including Spain and Austria, have seen their donation rate increase dramatically after introducing presumed consent, although Sweden, which also has such a scheme, has a lower donation rate than the UK.
The taskforce will also examine whether the family of somebody who has died should be given the final say on whether organs may be donated.
The British Medical Association, which advocates presumed consent, welcomed the government's decision to look into the issue further.
"We believe that when the taskforce looks at this issue in detail they will agree with us that a system of presumed consent with safeguards, will help to increase the number of donors available," said Dr Vivienne Nathanson, Head of BMA Ethics and Science.
While transplant groups inevitably back the scheme, several patient groups argue that it is not up to the state to decide what becomes of people's bodies when they die.
The Conservatives are also against the proposal, arguing it would be better to focus efforts on increasing the number of people on the organ donor list.
Liberal Democrat science spokesman Dr Evan Harris MP said far too many people were dying needlessly when many potential donors wanted their organs to be used to save lives.
"There must be a free vote on this issue when the Human Tissue and Embryo Bill comes before the House of Commons next year."
Roger Goss, co-director of Patient Concern, said: "Organ donation should be an altruistic gift that people should make freely.
"How can you have consented to something by failing to consent? Presumed consent, which normally means uninformed consent, relies on inertia to force a desired result."