Staffan de Mistura will brief the council behind closed doors on his meeting last week with Assad about a proposal to freeze hostilities in Aleppo, Syria's largest city, which is divided into a rebel-controlled west and government-held east.
This is de Mistura's first council briefing since he explained his freeze plan in October, and members want to know what kind of support, if any, it has received from Assad.
The UN estimates the conflict has killed 220,000 people.
Millions have fled to neighboring countries. De Mistura is the third in a series of UN envoys tasked with trying to find an end to the conflict. He was named to his post in July, not long after the Islamic State group launched an onslaught in Syria's north and east.
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De Mistura wants to see a UN-monitored "freeze zone" in Aleppo that will calm violence there, allow more humanitarian aid access and act as the first step toward a wider solution to the conflict.
But Aleppo-based opposition activists have expressed fears the government would exploit a truce to gather its forces to fight elsewhere, and they have questioned how a cease-fire could work with Islamic State fighters in the area.
And the Nusra Front, the al-Qaida affiliate in Syria, recently dismissed de Mistura's proposal as a conspiracy that would allow Syrian government forces to regroup for more assaults.
But a report released in November by the London School of Economics and the Madani organization examined 35 negotiations for local cease-fires in Syria over the past three years and concluded that local peace deals could be "the best hope" for alleviating civilians' suffering and provide a basis for a larger resolution to the conflict.