Negotiations on the handover of power in Iraq have reached an "advanced stage", said the UK government.
British forces in Iraq are currently subject to UK laws
Demands that coalition troops remain immune from prosecution by Iraqis after the handover of power will be dealt with in the new UN resolution.
BBC correspondent Jonathan Beale said UK and US forces want to remain under their own jurisdictions, even after the creation of a sovereign Iraq.
A government source said a draft of the resolution could go out this week.
But they stressed there was no agreement as yet on the question of immunity, which forms a small part of the overall negotiations.
Meanwhile a leaked memo suggests strong UK criticism of US tactics.
A Foreign Office memo to ministers, leaked to the Sunday Times, shows there are deep concerns within the British government.
It says the UK is struggling to convince US troops to adopt a more tactful approach in dealing with Iraqis.
Agreement on the resolution governing the return of Iraqi sovereignty, set for 30 June, needs to be reached in the next few weeks.
One of the biggest sticking points is the issue of whose laws the remaining foreign troops will be subject to - their own or Iraqi laws.
Giving them immunity is likely to be controversial after allegations of abuse by troops of Iraqis.
But, our correspondent reports, British and American governments want guarantees soldiers will remain under their own laws.
Under an order signed by the Coalition Provisional Authority, known as Order 17, coalition forces have immunity from prosecution.
Negotiators are seeking to prolong that arrangement after the transfer of power.
The latest pictures show detainees being threatened with dogs (AP Photo/Courtesy of The New Yorker)
Former British army commander Colonel Bob Stewart said troops would in any case continue to face court martials under international law or by national authorities.
"This is the normal way foreign forces are covered legally in a different country, because the law in Iraq is likely to be different from in the UK," he said.
It prevents soldiers facing severe penalties, such as the death penalty, for crimes considered more minor in their home state, he said.
But he criticised the "light" sentences for US soldiers who had already been found guilty at a court martial.
Many believe Iraqis should have the right to seek redress in their own courts or the sovereignty of the new state would be undermined.
A Foreign Office spokesman said the legal status of multinational forces after handover would be discussed by the military and the new interim government and covered in a new UN resolution.
The news has emerged as the Independent on Sunday reveals more claims of prisoner abuse allegedly carried out by members of the Queen's Lancashire Regiment.
It reports that the High Court is to consider claims the regiment carried out the "systematic torture of Iraqi civilians under the direction of an officer".
Five Iraqis said to have been arrested along with Baha Mousa, who died in British custody, have given detailed witness statements to the newspaper about their alleged ordeal.
A spokeswoman for the Army said there was already an investigation under way into the circumstances surrounding Baha Mousa's death, but could not comment on specific allegations.
She added that the Army would not tolerate abuse of prisoners in custody.