Army sources have told the BBC they favour Britain providing ground troops and helping to set up field headquarters in an operation which could involve up to 2,000 personnel.
The MoD has refused to make any official comment, but said an announcement was possible later this week.
A spokesman told BBC News Online: "We haven't even confirmed there's going to be such a mission. All we've said is that in principle, if asked, we would be willing to supply such a force."
Defence Secretary Geoff Hoon confirmed on Sunday that the government was prepared to supply troops and would "very seriously" consider a request to lead the force.
Meanwhile, a British Royal Engineer has been injured after stepping on a landmine near the Bagram airbase north of the Afghan capital Kabul.
The MoD said the soldier, who has not been named, was working as a member of an explosive ordnance disposal unit deployed to Bagram last month.
He was taken to a US military hospital on Thursday where his condition has been described as "stable".
Deadline
United Nations leaders have said they want a multi-national force in Afghanistan as soon as possible to help stabilise the region, rebuild and help aid organisations.
The BBC's Andrew Gilligan said any force would need to be in place by 22 December when the new Afghan power-sharing interim government is due to take office.
But he added: "It is vital British troops are properly protected."
On Saturday US Secretary of State Colin Powell said Britain, Germany and Turkey were among nations who had offered to lead the force.
On Sunday Mr Hoon told the BBC's Breakfast with Frost programme: "We have won the war and it is important that we win the peace and we play our part in the international community to rebuild Afghanistan."
He said the question of Britain leading the UN force should be put to the Cabinet and discussed and in Parliament.
'Death penalty'
The defence secretary told the programme Bin Laden would be handed over to the United States if captured by UK troops, with certain agreements, given the US policy of using the death penalty.
As a signatory to the European Convention on Human Rights, Britain does not extradite suspects to countries which use the death penalty unless assurances are secured that they will not face execution.
"But what is important, given the appalling horror that this man perpetrated in the United States on 11 September, is that he faces justice in US," he said.
Mr Hoon said the war in Afghanistan had gone better than expected.
He said: "We anticipated the Northern Alliance would be able to reoccupy those areas they dominated ethnically in the north of Afghanistan.
"What's gone much better than anyone could have expected is the revolt against the Taleban in the south".