The council will meet in the early hours of Monday (AEST) to decide on the draft resolution, despite resistance from Russia, Syria's ally and a veto-wielding Security Council member.
France circulated a draft text late Friday stating that the council is "alarmed" by the worsening humanitarian crisis in Aleppo and by the fact that "tens of thousands of besieged Aleppo inhabitants" are in need of aid and evacuation.
Thousands of trapped civilians and the last remaining opposition fighters in Aleppo were waiting for evacuations to resume on Saturday, a day after the operation was suspended by the Syrian government.
related reading
Aleppo evacuation suspended leaving thousands trapped
Syrian forces this week moved to assert full control over the east of the city, which had been held by opposition fighters since 2012.
French Ambassador Francois Delattre said the international presence prevents Aleppo from turning into another Srebrenica, where thousands of Bosnian men and boys were massacred in 1995 when the town fell to Bosnian Serb forces during the Balkan wars.
"Our goal through this resolution is to avoid another Srebrenica in this phase immediately following the military operations," Delattre told AFP.
The draft resolution would request that UN Secretary-General Ban Ki-moon quickly redeploy UN humanitarian staff already in Syria to the city "to carry out adequate, neutral monitoring, direct observation and to report on evacuations from besieged parts of Aleppo and protection of civilians inside Aleppo," according to a copy of the text obtained by AFP.
Ban would also ensure the deployment of further staff, according to the draft text, which demands that Syria grant access to the observers.
The UN chief would report to the council within five days on whether access has been granted by the Syrian government, which has repeatedly blocked UN access during the nearly six-year war.
Signs are held up as hundreds of Syrians and people standing in solidarity with them march for Aleppo on December 17, 2016 in London. (AAP) Source: AAP
Evacuation deal
A Syrian rebel official and a government official said early on Saturday the evacuation of Aleppo would resume and the two Shi'ite villages would be evacuated, as well as the wounded from two towns near the Lebanese border and east Aleppo.
But sources said negotiations between pro-government and opposition forces, plus their international backers, were still going on to finalise how the evacuations would take place and how many people would leave.
A senior Syrian rebel official from the powerful Ahrar al Sham group involved in the talks said the deal was being held up by Iran and its allied Shi'ite militias who were insisting people be allowed to leave the two besieged Shi'ite villages of Kefraya and al-Foua before letting the Aleppo evacuation happen.
"Iran and its sectarian proxies are using the humanitarian situation of our people in besieged Aleppo and preventing civilians from leaving until the evacuation of their groups in al-Foua and Kefyra," Munir Sayal, the head of the political wing of the movement, told Reuters in a telephone interview.
As darkness fell on Saturday afternoon and temperatures began to fall below freezing there was no sign the evacuation was happening.
A resident in Aleppo told Reuters that nobody had left the rebel-held enclave and no buses had entered. He said he had heard gunfire near where people were supposed to wait for buses.
The International Committee of the Red Cross (ICRC) said thousands of cold, scared and injured people were still in east Aleppo waiting to leave. It said it had received some indications that a deal would be reached soon.
The Syrian government official, part of the evacuations negotiating team, said: "It was agreed to resume evacuations from east Aleppo in parallel with the evacuation of (medical) cases from Kefraya and al-Foua and some cases from Zabadani and Madaya."
The towns of Madaya and Zabadani are blockaded by pro-government forces.
The operation to evacuate fighters and civilians from the last opposition-held area of Aleppo was suspended on Friday, its second day, after pro-government militias demanded that wounded people also be brought out of al-Foua and Kefraya, and protesters blocked a convoy on the road out of Aleppo.
The chaos surrounding the evacuation reflects the complexity of Syria's civil war, with an array of groups and foreign interests involved on all sides.
Aleppo had been divided between government and rebel areas in the nearly six-year-old war, but a lightning advance by the Syrian army and its allies that began in mid-November after months of intense air strikes deprived the insurgents of most of their territory in a matter of weeks.
Beaten and robbed
Numerous activists, rebels and east Aleppo residents shared reports and videos of people fleeing the sound of shooting, being detained and returning home badly beaten and robbed of their possessions near a checkpoint as they tried to leave the city on Friday.
Rebels said the previous evacuation deal was breached by pro-government militias who detained "hundreds" of people trying to leave, leading to some deaths.
A Syrian military source denied this, but said a convoy trying to leave was sent back.
"Now we are working on international guarantees to guarantee the safety of those who leave Aleppo so that such violations are not repeated," Syrian rebel official al-Farouk Abu Bakr told news channel al-Arabiya al-Hadath from Aleppo on Saturday.
Related reading
Syria crisis: How you can help those in need
An activist and teacher inside rebel-held Aleppo, Wissam Zarqa, told journalists via a messaging app that he spent Friday in the cold with his family hoping to leave.
He said he did not feel safe trying to flee Aleppo after hearing about the attack on the convoy.
The Syrian Arab Red Crescent (SARC) and the ICRC said guarantees were needed to protect people.
"We're ready to resume facilitating the evacuation according to our humanitarian mandate. But we now expect all the parties on the ground to provide us with solid guarantees in order to keep the operation going," said Marianne Gasser, head of the ICRC in Syria.
WATCH: Evacuation began
No buses yet
A military news outlet run by Damascus's ally Hezbollah said evacuation buses were heading to the two villages.
But the Syrian Observatory for Human Rights, which monitors the war, said no buses or ambulances had entered al-Foua or Kefraya, where it says there are around 20,000 people, of whom roughly 4,500 are pro-government fighters.
The Observatory said 8,000 people, including some 3,000 fighters and more than 300 wounded, left Aleppo in convoys of buses and ambulances in the evacuations that began on Thursday morning.
WATCH: Samantha Power speech in the UN Security Council
Rebel officials say the numbers evacuated are much lower, with no fighters having left.
The UN says around 30,000 people remain in rebel-held Aleppo, of whom a number would be taken to Idlib province, which is mostly controlled by hardline Islamist groups, and the rest would go to government-held city districts.
Idlib is already a target for Syrian and Russian air strikes but it is unclear whether the government will push for a ground assault or simply seek to contain rebels there for now.
Turkey has said Aleppo evacuees could also be housed in a camp to be constructed near the Turkish border to the north.
Overnight bombing
The Observatory said war planes bombed insurgent-controlled areas west of Aleppo overnight and north of Aleppo on Saturday.
Syrian state media reported on Saturday that a number of fighters south of Damascus had surrendered their weapons to the state in the towns of Zakiya and al-Deirkheyba as part of local truces.
Through a series of so-called "settlement" agreements and army offensives, the Syrian government, backed by Russian air power and Iranian-backed militias, has been steadily suppressing armed opposition in the capital city's suburbs.
Russian President Vladimir Putin, Syria's most powerful ally, said on Friday he was working with Turkish President Tayyip Erdogan to try to start a new round of Syrian peace talks aimed at securing a nationwide ceasefire.
A senior Syrian opposition leader, Riyad Hijab, said he was willing to attend the talks if the aim was to set up a transition government.
Assad has ruled out stepping down as part of a political solution to the war.
Aleppo, a once-flourishing economic center with renowned ancient sites, has been pulverised during the war that has killed more than 300,000 people, created the world's worst refugee crisis and allowed for the rise of Islamic State.
Even with victory for Assad in Aleppo, the war will be far from over.
Insurgents retain their rural stronghold of Idlib province as well as other territory in western, northern and southern Syria, and the jihadist Islamic State group holds swathes of the east and recaptured the ancient city of Palmyra this week.
