Opposition advances have given the issue new urgency
The statement to be adopted by the foreign ministers of the so-called six-plus-two countries - Afghanistan's neighbours plus Russia and the United States - backs efforts to oust the Taleban.
But, as the BBC's Eurasia analyst Pam O'Toole reports, the meeting at the UN General Assembly in New York is not expected to specify who should take over if the Taleban are overthrown - a matter of heated debate.
Afghanistan's neighbours - China, Pakistan, Iran, Tajikistan, Turkmenistan and Uzbekistan - have always argued over Afghanistan's future.
Unprecedented unity
They have come together to issue the statement following efforts of the UN special representative for Afghanistan, Lakhdar Brahimi, who recently toured the region to try to unite them.
Mr Brahimi is also expected to attend the six-plus-two meeting.
The draft statement calls on the Afghan people to establish "a broad-based, multiethnic, politically balanced, freely chosen Afghan administration, representative of their aspirations and at peace with its neighbours".
"This administration must be able to meet the needs of the Afghan people and respect human rights, regional stability and Afghanistan's international obligations, including suppression of trade in narcotics," it says.
For any political solution to work, the new government has to have the backing not only of the Afghan factions, but of the various countries that support them, our correspondent says.
New urgency
The search for a post-Taleban government took on new urgency after the Northern Alliance opposition forces captured the key northern city of Mazar-e-Sharif and turned their sights on the capital, Kabul.
The United States has been backing a proposal for a council of Afghans, headed by Afghanistan's former king, Zahir Shah.
The council would act as an interim government and would convene a loya jirga, or grand assembly, of Afghans to select a future head of state.
But there has been little progress on getting that council together.
Interim administration
French President Jacques Chirac said a resolution France and the UK planned to present at the Security Council would be "very close" to a French proposal calling for a UN-backed transitional administration with the involvement of the 87-year-old former monarch.
Iran, another main backer of the Northern Alliance, is unenthusiastic about the former king playing a prominent role in any interim administration.
According to a senior Iranian diplomatic source, Tehran would prefer to see an interim administration run by Afghan technocrats and supported by the United Nations prepare the ground for a loya jirga.
The question of who should be represented in an interim administration - and by whom - is also a matter of contention.
Pakistan, the Taleban's main backer, says any interim body should reflect the fact that Pashtuns are Afghanistan's biggest ethnic group.
It would like to see some kind of moderate Taleban presence there, but there are disputes about who could fill such a role.
Saudi Arabia's foreign minister, Prince Saud al-Faisal, has also submitted "a concept paper presenting a plan of action aimed at bolstering stability in the country", a UN statement said.
But so far there is no sign that the UN or anyone else has come up with a formula acceptable to all sides.
And there have been voices arguing that the six-plus-two group is not suitable for monitoring Afghanistan's future, and that it should be a larger forum, including representatives of the European Union.