However, a Lebanese official close to Damascus said Makdad had been sent to seek Russian advice on a possible agreement.
He said Syrian officials were upbeat after talks with Brahimi, the U.N.-Arab League envoy, who met Foreign Minister Walid Moualem on Tuesday a day after his session with Assad, but who has not outlined his ideas in public.
"There is a new mood now and something good is happening," the official said, asking not to be named. He gave no details.
Russia, which has given Assad diplomatic and military aid to help him weather the 21-month-old uprising, has said it is not protecting him, but has fiercely criticized any foreign backing for rebels and, with China, has blocked U.N. Security Council action on Syria.
A Russian Foreign Ministry source said Makdad and an aide would meet Foreign Minister Sergei Lavrov and Mikhail Bogdanov, the Kremlin's special envoy for Middle East affairs, on Thursday, but did not disclose the nature of the talks.