UN spokesman Martin Nesirky yesterday said Brahimi would brief the council sometime during the week of March 10-16.
Western diplomats suggested a March 14 date for the Security Council meeting and said Brahimi might also address the General Assembly.
A second round of Geneva negotiations to find a political solution to the conflict ended in discord February 15.
Brahimi broke off the talks, known as Geneva II, without setting a date for another round.
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"We still think the Geneva II framework is extremely important, but maybe one can combine different approaches," the diplomat said.
The Geneva II talks broke down over basic disagreements about an agenda, with the Syrian government insisting on giving priority to terrorism while the opposition wanted to concentrate on putting in place a transitional government that would strip President Bashar al-Assad of all or part of his powers.
Sigrid Kaag, the mission's coordinator, said her team is "studying the proposed timetable and its implications, and she expects to say more in the coming days," Nesirky said.
Diplomats said Kaag was supposed to brief the Security Council on her mission March 5.
The Security Council has given the Syrian regime until June 30 to destroy all its chemical weapons but Damascus has already missed many deadlines.