Israel seized the strategically important plateau from Syria in the 1967 Arab-Israeli war, and annexed it in 1981.
Opponents warn that a deal with Israel could increase tensions between Syria and Iran.
Marwan Bishara, Al Jazeera's senior political analyst, said that Turkey has been playing a mediation role since the Justice and Development (AK) party came to power four years ago.
"I think some in Washington and Tel Aviv are interested in such a Turkish role, and certainly Syria is pleased that its northern neighbour - the one that it had animosity with for many, many decades - is now friendly ... and would like to mediate a possible agreement," he said.
The indirect contact comes despite recent tensions, in part stemming from an Israeli air raid last September on a Syrian military facility.
Damascus has denied claims that Israel hit a Syrian nuclear installation developed using North Korean technology.
Thursday's closed-door hearings of the US House Intelligence Committee regarding the bombed site were closely followed by senior officials in Israel, the country's Haaretz daily said on Saturday.
Senior Israeli defence sources cautioned that the Syrians may now reconsider and decide to retaliate against Israel in some way.
Defence sources said that there was still the risk of an escalation in the area and warned that Israel must be cautious and avoid embarrassing al-Assad unnecessarily, Haaretz said.
'Ready for peace'
Earlier this week, Buthaina Shaaban, Syria's minister for expatriate affairs, had confirmed that the Israeli talks offer was put forward through Erdogan.
"The Turkish prime minister has conveyed to Syrian president Bashar al-Assad that Ehud Olmert is ready for peace with Syria on the basis of international resolutions and the return of the whole Golan Heights to Syria," Shaaban told Al Jazeera on Wednesday.