Britain's Defense Ministry says there's no precise timetable but there could be a further winding down of its role in southern Iraq next month.
The London Sunday Times reports the handover of security responsibility for Basra to the Iraqis could come in October.
Britain has been in charge of security in the South since joining the US in the 2003 invasion. It's already transferred security responsibility to Iraqis in 3 of the four southern provinces. Basra would be the last.
Britain has withdrawn hundreds of troops from Iraq, but still has a force there of about 5,500, mainly outside Basra.
The major oil hub has been the scene of frequent battles between Shiite factions jockeying for power. Just last weekend, militiamen loyal to anti-American cleric Muqtada al-Sadr (mook-TAH'-duh al SAH'-dur) seized control of a joint police command center after British soldiers left.