Diplomatic sources said that the vote was scheduled for 10 a.m. in New York, Efe news reported.
The initiative required UN staff to coordinate and observe the departure of inhabitants of eastern Aleppo.
Thousands were evacuated from the former opposition stronghold, recaptured almost in its entirety by pro-government forces.
The process, however, was stopped on Friday and people were now waiting for the resumption of the agreement between the parties.
Western countries have denounced the alleged abuses against some of the evacuees and considered it fundamental to have international observers present during the process.
Russia has expressed skepticism about the possibility of the UN monitoring the evacuations and said that deploying observers would take weeks.
French authorities, however, believe that the mission could be carried out with UN personnel already in the area.
Both France and the US warned Moscow that if it blocks the adoption of the resolution, they would convene a special session of the UN General Assembly to put pressure on Damascus and its allies.
So far in the conflict in Syria, the Russian delegation has used its veto power six times to paralyze initiatives on war in the Security Council.