The mission's mandate expires Friday, and the Council has been divided over whether a new resolution should include a threat of sanctions against President Bashar al-Assad's government.
Britain, France, Germany and the United States are pushing for a 45-day renewal of the U.N. observer mission in Syria along with a threat of sanctions.
Russia has promised to veto that version. Its proposal calls for a longer extension of the mission, but no sanctions.
China has backed Russia in blocking previous Western-backed resolutions calling for tough action on Syria.
U.N. Secretary-General Ban Ki-moon is meeting with Chinese leaders in Beijing. A U.N. statement said he expressed hope that the Security Council will unite to help end the bloodshed in Syria and help the country's people begin working toward a Syrian-led transition.
China's official People's Daily newspaper ran a commentary Tuesday rejecting foreign intervention in the Syrian crisis.
Violence continues around Damascus
The push for consensus comes amid continuing violence in Syria, including days of clashes between rebels and government forces in the capital, Damascus
It has been the heaviest period of fighting in the city since the revolt against Assad began 16 months ago.
Amateur video posted online Tuesday appeared to show panicked Damascus residents fleeing the fighting earlier this week. The video has not been independently verified.
