Prime Minister David Cameron has set a deadline of the end of December 2014 for Britain to stop all of its combat operations.
But it is understood that up to 200 members of the UK's special forces could stay on to help combat terrorism, the BBC reported.
British troops have been in Afghanistan since the US-led invasion in 2001.
Britain plans to withdraw 500 soldiers from its 9,500- strong force this year, with Afghan security forces due to take over responsibility for security by the end of 2014.
The official made the disclosure ahead of a NATO summit in Chicago, which is expected to focus on Afghanistan.
The official said: "As we've said previously, British forces will not remain in a combat role in Afghanistan beyond 2014.
"The majority of forces that remain in Afghanistan will be in a training and mentoring role, for example at the Afghan Officer National Training Academy.
"But I wouldn't rule out a small number of forces playing a counter-terrorism role if needed.
"This would be in keeping with how we are working to protect ourselves from the counter terrorism threat emanating from other parts of the world, such as the Arabian Peninsula," the official said.
Last month, UK Defence Secretary Philip Hammond said the UK would fund Afghan security forces after British combat operations in their country cease.
He said the UK would give 70 million pounds a year to a four billion pound international fund to stop Afghanistan once again becoming a "safe haven" for terrorists.
The first 70 million pound payment would be made in 2015, he said.
