The sources said that in their talks yesterday the two men addressed the question of whether the coalition would formally endorse Alkhatib's peace initiative.
The Muslim Brotherhood, which controls a large bloc within the Islamist-dominated coalition, is against the initiative.
But the Brotherhood, the only organized political force in the opposition, is unlikely to challenge Alkhatib's authority directly, with his initiative gaining popularity in Syria, the sources said.
The Syrian authorities have not responded directly to Alkhatib's initiative – formulated in broad terms last month. But Information Minister Amran al-Zubi on Friday repeated the government's line that the opposition was welcome to come to Damascus to discuss Syria's future in line with Assad's proposals for a national dialogue.
Alkhatib has headed the Syrian National Coalition since it was founded last December in Qatar with Western and Gulf backing. He has quietly built a student following and links with civic and religious figures across Syria.
His latest offer of talks coincided with opposition reports of fighting moving closer to central Damascus, after a rebel push into the east of the capital last week.
The Local Coordination Committees, a network of grassroots activists, said clashes broke out yesterday in the al-Afif neighbourhood of Damascus, which is adjacent to a presidential complex.
The organization said 77 people were killed in Syria yesterday, including 16 people who it said had been executed by Assad's forces in the eastern city of Deir al-Zor. Such reports are impossible to verify as Syria severely restricts access for independent media.
The war is pitting Mr. Assad's minority Alawite sect, an offshoot of Shi'ite Islam that has dominated Syria since 1960s, against the Sunni majority that has led the protest movement.