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When Alkhatib made his offer of talks last month, he made this conditional on the authorities starting to release tens of thousands of political prisoners jailed since the eruption of the 22-month uprising.
The United Nations said on Friday that it saw a glimmer of hope in Alkhatib's offer.
UN Under-Secretary-General for Political Affairs Jeffrey Feltman said the offer was "the most promising thing we've heard on Syria recently".
Yesterday, Alkhatib spelled out ideas on a venue for talks.
He said: "If the regime is so concerned about sovereignty and does not want to venture out of Syrian territories, then there is a suitable solution, which is the liberated land in northern Syria."
He added: "There is an important question. Will the regime agree to leave with the minimum of blood and destruction?"
Syria's uprising, which started as peaceful protests against four decades of autocratic rule by Assad and his late father, has turned into a violent sectarian conflict.
Freedom for political prisoners is an important issue for the opposition. Alkhatib said even centrist opposition figures who were willing to talk with Assad, such as Abelaziz al-Khayyer, a veteran Alawite human rights campaigner, have been jailed.
"The regime deals with the demands to release the political prisoners, especially the women, in a totally inhumane way," Alkhatib said. "Despite two years of savage killing, the regime is still trying to buy time."
The scion of a religious family who have historically been custodians in the Umayyad mosque in Old Damascus, Alkhatib was a proponent of a negotiated solution while he was in Syria. But he was jailed several times during the revolt in secret police dungeons and was forced to flee the country.
Alkhatib said the regime missed a "rare opportunity' by not agreeing to release women prisoners by a deadline he had set for yesterday, but that he was compelled morally to continue to try to negotiate a peaceful exit for Assad.