The US is expected to request RAF aircraft
Prime Minister Tony Blair and his ministers will then have to decide what role the UK could play in any military response to the attacks on the World Trade Centre and the Pentagon.
Defence sources say a decision on the exact nature of UK involvement will be made by the end of this week, although Downing Street is stressing that the plans are far from finalised.
It is believed the UK has been asked to supply small numbers of ground troops, mainly special forces.
The US is also understood to have asked for reconnaissance and attack aircraft from the RAF.
BBC correspondent Andrew Gilligan said: "In a purely military sense, there's little the UK can offer that America doesn't already have.
"But the presence of non-Americans in the military operation is considered politically vital."
Casualty warning
The briefing, taking place as the United States prepares to show its allies evidence linking Osama Bin Laden to the 11 September attacks, follows warnings from ministers over the possibility of British casualties.
Foreign Secretary Jack Straw, speaking before heading off on his diplomatic mission to Iran, told the BBC people above all had to expect "a great deal of uncertainty".
"But it is very difficult in these extraordinary circumstances, where this is not any kind of classic war, but we're fighting non-state terrorists supported by a semi-state.
"The circumstances are very uncertain and, of course, people are going to be worried and above all those in the services and service families.
"There will be risks and there may well be casualties, and that is a very heavy responsibility on all of us who are having to make these decisions, but it is obviously very, very much worse for those taking the risks and for their families."
On Sunday Northern Ireland Secretary John Reid said, as America's biggest ally, the road ahead "may involve sacrifices, not only here at home, with inconvenience and possible danger".
He said any unwillingness to make the necessary sacrifices would mean "capitulating" to terrorism: "I don't believe we can do that."
The ministry of defence has played down newspaper reports that crack SAS troops are already inside Afghanistan working with the anti-Taleban Northern Alliance.
Several Sunday newspapers reported that a four-man unit had already been involved in a fire-fight with the Taleban near Kabul.
US build-up
The US has repeatedly warned the ruling Taleban in Afghanistan that they will face military action unless they hand over Osama Bin Laden, the chief suspect for the attacks.
US air and sea power continues to be massed in the region.
The Pentagon activated another 5,172 reserve troops at the weekend, a day after eight B-52 heavy bombers began departing.
Officials said another deployment of planes was expected, bringing to more than 200 the number of planes that would join about 350 aircraft already in the region.
It is thought that about 20,000 UK military personnel carrying out exercises in Oman could be redirected to Afghanistan if required.