The draft text, obtained by AFP, states that the "only sustainable solution to the current crisis in Syria is through an inclusive and Syrian-led political process that meets the legitimate aspirations of the Syrian people."
The measure draws heavily on statements agreed during previous talks in Geneva and Vienna by calling for an "inclusive transitional governing body with full executive powers" in Syria.
It asks the United Nations to bring the Syrian government and the opposition to the table for formal negotiations on a political transition "with a target of early January 2016."
The draft resolution, however, does not touch on one of the most contentious issues in the peace effort: the fate of Syrian leader Bashar Assad.
Ahead of the council meeting, U.S. President Barack Obama reaffirmed the U.S. stance that Assad must leave power during his Washington year-end news conference.
"I think that Assad is going to have to leave in order for the country to stop the blood(shed), for all the parties involved to be able to move forward in a nonsectarian way," Obama said. "He has lost legitimacy in the eyes of the country."
Obama said Assad's remaining in power, after having chosen to "slaughter" his people rather than pursue an inclusive political transition, "is not feasible."
"As a consequence, our view has been that you cannot bring peace to Syria, you cannot get an end to the civil war unless you have a government that it is recognized as legitimate by a majority of that country. It will not happen," he said.
The diplomatic balancing act aims to keep both Moscow and Riyadh on board as big powers aim to build momentum for peace talks and a ceasefire.
Syria's main opposition group, the Syrian National Coalition, said however that achieving a ceasefire by January 1 was unrealistic and demanded that Russia halt air strikes as part of that truce.
Assad, in his interview with Dutch television, turned sarcastic when asked whether he was comforted that Washington's stance on his departure was seemingly softening. "I was packing my luggage. I had to leave, but now I can stay," he said. Read the full story here.