Final negotiations between the two governments are under way, with British Prime Minister Gordon Brown expected to make an announcement by Christmas, Sky News reported.
British forces have been based in southern Iraq since 2003.
Brown said there has been no change in the nation's policy "to continue and finish the work we have agreed to do in Iraq. Once we have done these things, there will be that fundamental change of mission," Sky News said.
"We'll continue to work closely with the government of Iraq but we will see a significant drawdown of British troops as a recognition of the progress and success that's been enjoyed ... in Basra," said Douglas Alexander, Britain's international development minister.
Iraqi officials have been pushing for foreign troops to pull out of Iraq and are in talks with the United States about the future role American troops will have in the country once the U.N. mandate authorizing an international military presence in Iraq expires at the end of 2008.