The governing coalition will not order its lawmakers to block the proposals and instead they will be given a free vote according to conscience, a spokesman said.
The draft legislation will come before parliament in the next four months, The Sunday Telegraph newspaper said.
It remains a criminal offence -- punishable by up to 14 years' imprisonment -- to help someone take their own life, under the 1961 Suicide Act.
Four years ago, the director of public prosecutions (DPP), who heads England's state prosecution service, issued guidelines which said anyone "acting out of compassion" while helping a loved one to die was unlikely to be charged.
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Prime Minister David Cameron of the centre-right Conservatives and Deputy PM Nick Clegg of the centrist Liberal Democrats have both in the past voiced opposition to amending the law.
But a Ministry of Justice spokesman said: "The government believes that any change to the law in this emotive and contentious area is an issue of individual conscience and a matter for parliament to decide rather than government policy."
Lord Charles Falconer of the opposition Labour Party is bringing his Assisted Dying Bill before parliament's upper House of Lords in the coming months.
If it passes an initial Lords vote, it will go to the elected lower House of Commons.
Falconer says the DPP guidelines encourage "amateur assistance only" and are driving people to clinics in Switzerland, where assisted dying is permitted.
Assisted suicide allows a doctor to provide a patient with all the necessary lethal substances to end their life, but lets them carry out the final act.
Euthanasia goes a step further, and allows doctors themselves to administer the lethal doses of medicine. This practice is legal in the Netherlands, Belgium and Luxembourg.
Betty Boothroyd, a former Commons speaker who now sits in the Lords, said Wednesday the current legal situation on assisted dying makes a "mockery" of English justice.
"The current law should be repealed to make way for a better one," she told the chamber.
"This is a moral issue whose time has come and parliament should resolve it.