A slightly amended text was circulated to council members late Thursday but it was unclear whether Russia would support the measure which has been under negotiations for two weeks.
The council will meet to vote at 1 p.m.
Russian Ambassador Vassily Nebenzia told a council meeting on Thursday that there was “no agreement” on a truce and presented a new raft of amendments.
Negotiations have dragged on at the United Nations as hundreds of Syrians have died in a fierce government air campaign in the rebel-held enclave of Eastern Ghouta.
Sweden and Kuwait presented the proposed measure on February 9 but have been unable to overcome resistance from Russia, Syria’s military ally.
Diplomats said it was not known whether Russia would use its veto to block the draft resolution.
The latest text softens language in a key provision to say that the council “demands” a ceasefire instead of “decides.”
It also specifies that the ceasefire will not apply to “individuals, groups, undertakings and entities associated” with Al-Qaeda and the Islamic State group. A previous version simply mentioned the two terror groups.
More than 400 people have been killed in the five-day assault by the government on Eastern Ghouta, where UN Secretary-General Antonio Guterres said 400,000 Syrians are living in “hell on earth.”
During the meeting called by Russia on Thursday, Nebenzia told the council that it should agree on a ceasefire that is “feasible” and not make decisions that are “severed from reality.”
The ambassador circulated an amended text which specified that aid deliveries would happen “as security conditions permit” and added that “foreign military forces can operate in Syria only in coordination with its official authorities,” according to the document obtained by AFP.
Those provisions were not however included in a new draft that followed last-ditch negotiations late Thursday.
A Security Council diplomat earlier said “the Russian amendments are unacceptable.”
The United States, Britain and France have pushed for a quick vote to address the dire situation on the ground as Syrian warplanes pounded Eastern Ghouta.
The US State Department said Russia had a “unique responsibility for what is taking place” in the rebel-held enclave near Damascus.
“Without Russia backing Syria, the devastation and the deaths would certainly not be occurring,” spokeswoman Heather Nauert told journalists.
Outside UN headquarters in New York, a coalition of aid groups put up three billboards, inspired by the film “Three Billboards outside Ebbing, Missouri” that said “500,000 dead in Syria. And still no action? How come Security Council?”
The draft resolution would pave the way for the truce to go into effect 72 hours after the adoption of the measure and for aid deliveries and medical evacuations to begin 48 hours after that.
It demands the immediate lifting of all sieges including in Eastern Ghouta, Yarmouk, Foua and Kefraya and orders all sides to “cease depriving civilians of food and medicine indispensable to their survival.”
In a concession to Russia, the draft was amended during tough-going negotiations last week to specify that the ceasefire does not apply to the Islamic State group or Al-Qaeda.
That would allow the Syrian government offensive to continue against Al-Qaeda-linked jihadists in Idlib, the last province in Syria outside the control of Damascus.
French Ambassador Francois Delattre warned that failure to act to help Eastern Ghouta would deal a blow to UN credibility and could sound “the death knell of the United Nations.”
More than 340,000 people have been killed and millions driven from their homes in the war, which next month enters its eighth year with no end in sight.