Russia is expected to use its veto to block the French-drafted measure backed by the United States and Britain that also provides for a halt to all military flights over Aleppo.
The council will then move to a second vote on the Russian-drafted text that calls for a ceasefire but makes no specific mention of stopping the aerial bombardment of Aleppo.
British Ambassador Matthew Rycroft dismissed the Russian draft text as a political ploy.
“This is a cynical attempt to divert attention away from the need to stop the bombing of Aleppo,” he said.
The Russian text, obtained by AFP on Friday, “urges immediate implementation of the cessation of hostilities, in particular in Aleppo” and demands that all parties allow deliveries of humanitarian aid.
At least 250,000 people are living under siege in rebel-held east Aleppo, and facing almost-daily heavy bombing since the Russian-backed Syrian army launched an offensive to retake the city last month.
Council members have been holding negotiations for the past week on the French proposal for an end to the bombing of Aleppo, access for aid deliveries and a ban on military flights over the city.
But Russian Ambassador Vitaly Churkin said the measure was “hastily put together” and suggested it was “not designed to make progress… but to cause a Russian veto.”
“I cannot possibly see how we can let this resolution pass,” he told reporters when asked whether he would resort to the veto as one of the council's five permanent members.
If Russia blocks the draft, it will be Moscow's fifth veto of UN resolutions on Syria.
The Security Council met in emergency session at Russia's request to hear UN envoy Staffan de Mistura outline proposals to allow jihadist fighters to leave Aleppo.
The Russian-drafted text welcomes the envoy's initiative and calls on UN Secretary-General Ban Ki-moon to present a detailed plan that could be endorsed by the Security Council.
A Security Council diplomat, who asked not to be named, said the Russian “resolution on the surface looks like a lot of constructive language that draws from previous resolutions and the French draft, but the key point is
that it does not call for an end to the aerial bombardment.”
He said the “vast majority” of council members want “an immediate end to the indiscriminate bombing of civilians in Aleppo.”
The decision to move to a vote followed days of shuttle diplomacy by French Foreign Minister Jean-Marc Ayrault, who traveled to Moscow and Washington to secure agreement on the draft resolution.
Ayrault, who will attend the council meeting on Saturday, said the vote will be a “moment of truth for all the members of the Security Council.”
“Do you want a ceasefire in Aleppo, yes or no? And the question is in particular for our Russian partner,” the foreign minister said in Washington.
European countries and the United States are shifting toward a tougher line on Russia over its actions in Syria and have suggested that sanctions could be imposed. The United States on Friday called for Russia and Syria to be investigated for war crimes for the bombing of hospitals.
“Russia and the regime owe the world more than an explanation about why they keep hitting hospitals and medical facilities, children and women,” US Secretary of State John Kerry said.
Now in its sixth year with more than 300,000 dead, the war in Syria has raged on as the Security Council has been divided between Russia, which backs President Bashar al-Assad, and western powers supporting opposition rebels.