The troops would be sent ahead of presidential elections
Prime Minister Gordon Brown is offering to send more British troops to serve on operations in Afghanistan.
The troops would be sent to provide security ahead of the country's presidential elections in August, UK officials said.
They said the increase would only be temporary and would most likely involve hundreds, not thousands, of troops.
But the offer is conditional upon other Nato members also being willing to send military units to help security.
A UK official said: "There is obviously a risk of the Taleban wanting to disrupt these elections. The smooth running of these elections is clearly in our interests.
Gary O'Donoghue, BBC political correspondent
Today's suggestion by the UK government that it was prepared to consider a temporary increase in troops in Afghanistan is clearly designed to put pressure on other Nato allies to step up to the plate.
There's been frustration in London for some time that some Nato governments are not pulling their weight in what's called "burden-sharing".
One senior government source said it was made difficult by the fact that some countries had "caveats" attached to its contingents in Afghanistan such as the Germans' refusal to fly helicopters at night.
But British officials have been sounding a more optimistic note, with one suggesting that Gordon Brown anticipated getting a positive response to his offer.
That is undoubtedly down to the Obama effect, with many countries now desperate to demonstrate goodwill towards the new president.
"The prime minister will be making clear in discussions that we will consider a temporary increase in our troop numbers to cover the election period subject to appropriate burden-sharing.
"This will be a temporary deployment in order to deal with security issues arising from the elections. This is not at this point a decision. This is something that remains under consideration."
Officials have also made it clear that any potential deployment is not connected to a wider debate over Britain sending more troops as part of a permanent deployment to Afghanistan.
The extra troops - it is thought around the size of a battalion - would come home straight afterwards, the BBC's security correspondent Frank Gardner said.
The temporary deployment offer was made as Mr Brown flew to the Nato summit in Strasbourg.
Earlier US President Barack Obama urged better use of Nato resources in Afghanistan, saying al-Qaeda was a greater threat to Europe than to the US.
The UK currently has some 8,000 troops serving in the country, most of them in the southern province of Helmand.
Last week, Mr Obama published plans to send an extra 21,000 American troops to Afghanistan.