Staffan de Mistura is making the rounds ahead of another meeting in Vienna of key players with influence in Syria, including the United States, Iran, Saudi Arabia and Russia.
De Mistura will brief the 15-member council on Tuesday.
The UN envoy said in Moscow this week that the United Nations was ready to bring together the Syrian government and opposition for talks in Geneva.
All players however need to agree on the list of opposition members and government representatives who will be allowed to take part.
At the first meeting in Vienna last week, the participants agreed to ask the UN to broker a deal to pave the way for a new constitution and elections.
The Vienna talks mark the most significant international effort to date to end the four-year war. It has left 250,000 people dead and triggered Europe's worst refugee crisis since World War II.