The newspaper said it has learned the proposal to accelerate Britain's troop withdrawal will be one of three options put before Prime Minister David Cameron at next week's National Security Council meeting.
At least two senior cabinet members are said to favor the idea.
The plan would cut British troops from 9,000 to 5,000 during 2013, with a similar number to be pulled out the following year when NATO ends its combat role in the country, the newspaper said.
Martin Bashir resigns from MSNBC over Sarah Palin comments
Ron Burgundy interviews Peyton Manning on SportsCenter