He added that some rebels also "agreed to the principle" of a cease-fire.
But whether the words lead to any kind of peace remains uncertain.
The U.N.-Arab League special envoy to Syria spoke from Cairo after a recent trip to Damascus.
But Syrian Foreign Ministry spokesman Jihad Makdissi said that from his perspective, nothing was set in stone.
"The issue of halt(ing) the military operations during the Eid al-Adha holiday is still under study by the general command of the military and the armed forces," Makdissi told CNN Wednesday. "A final decision will be issued tomorrow in this regard."
The Syrian government has previously promised to withdraw its forces, but violence continued unraveling.
Earlier this year, President Bashar al-Assad's government agreed to a six-point peace plan laid out by Brahimi's predecessor, Kofi Annan. But reports of violence by both troops and rebels raged on.
In other developments:
Reports of fresh carnage on the ground did little to support the notion of an imminent cease-fire.
Both dissidents and government forces blamed each other for a "massacre" in the city of Douma.
The opposition Syrian Observatory for Human Rights said at least 16 bodies, including some of children, were found. Activists blamed the attacks on government forces, the observatory said.
Syrian state-run media gave a different account:
"Terrorist armed groups committed a heinous massacre in the city of Douma, resulting in the killing of nine men, three children and one woman -- all slaughtered by knives," state TV reported.
Refugee crisis mounts in Jordan
The hundreds of thousands of Syrians who have fled across borders can sleep without fear of further attack. But they're also causing serious strains on their host countries, such as Jordan.
Providing healthcare to "the Syrian brothers" has drained resources and put enormous pressure on Jordanian hospitals and clinics, Minister of Health Abdullatif Wreikat said, according to Jordan's official Petra news agency.
He said Jordan, Syria's southern neighbor, now has more than 200,000 refugees and needs more aid.
Wreikat said the kingdom has made significant strides in fighting contagious diseases, but fears a decline "as some diseases had spread among the Syrian refugees," Petra reported.
The Health Ministry has provided 50,000 doses of vaccines against diseases to Syrian children at the Zaatari refugee camp, in addition other health services, a ministry official said, according to Petra.