The supporters of a new United Nations resolution on Iraq hope it will be passed next month, before the American-led coalition transfers power to the Iraqis at the end of June.
The British and Americans are keen to see a resolution which would bless the transitional arrangements.
Brahimi is drawing a plan for the handover of power
However it would not go far enough for Spanish Prime Minister Jose Luis Rodriguez Zapatero, who has already announced he is pulling out his troops because his call for the UN to take over was unlikely to be fulfilled.
There is no suggestion that any new resolution would put the UN in charge of running the country or security, or bring in blue-helmeted UN Peacekeepers.
British Prime Minister Tony Blair, who held talks with UN Secretary General Kofi Annan in New York, said they would need a new UN Security Council resolution "that will allow us to point the way towards political transition in Iraq".
The British ambassador to the UN, Sir Emyr Jones Parry, outlined his ideas during closed talks between Security Council members.
He told them he would like the resolution to recognise the end of the occupation, bless the new interim government, authorise a continuing international military force and outline the UN's future role in Iraq.
There appears to be broad agreement among Security Council members that there should be a new resolution but there could be some debate about its contents.
There were concerns about President Bush's comments that he would like a new resolution to help other nations to decide to participate.
Security Council members, particularly those who opposed the war, do not want the UN to be seen as simply providing political cover to persuade more countries to join the coalition.
The UN's role in the transition process is becoming increasingly prominent.
The UN special envoy to Iraq, Lakhdar Brahimi, is, at the request of the Americans, drawing up a plan for the transition of power to the Iraqis.
This followed widespread rejection among Iraqis of the American plan to chose the government through caucus-style meetings.
Mr Brahimi has so far suggested an outline structure which would include a president, two vice-presidents, a prime minister and ministers aided by a consultative assembly to be chosen after the transfer of power.
The government will be selected by the UN, the Iraqi Governing Council, the coalition and a group of Iraqi judges although the procedure has not been finalised.
Mr Brahimi is due to brief the Security Council about the plans later this month.
A resolution is unlikely until the transitional arrangements are agreed.
The resolution would also outline the UN's future role in Iraq.
British diplomats say that as well as helping with the transfer of power, they would also like UN involvement in drawing up the constitution and arranging elections due by next January.
However, Secretary General Annan has made it clear that the current insecurity makes a large-scale return of UN staff to Iraq unlikely in the near future.
The UN's international staff were withdrawn from Iraq last October following two suicide attacks on UN headquarters in Baghdad.