The talks on a faster withdrawal were prompted by criticism from Chancellor George Osborne, who challenged the Army's presence in Afghanistan at a meeting of the National Security Council last month, The Daily Telegraph reported Friday.
Osborne questioned the proposed plan for withdrawal, asking why British forces should not come home now.
Ministers and military chiefs are debating the timetable for removing the last 9,000 British troops from Afghanistan. No decision about withdrawals in 2013 has been made, and a final decision may not be made until February, the report said.
Prime Minister David Cameron said this week "nearly all" British troops would be out of Afghanistan by the end of 2014.