Legislators in Tel Aviv revealed the details of the proposal on Sunday as Syria raises the possibility of resuming negotiations.
According to Danny Yatom, who headed then-Prime Minister Ehud Barak's political staff, Barak was offering to withdraw from all of the captured Golan Heights down to the Sea of Galilee.
Yatom claims all land was offered back except for a small symbolic Israeli presence on the east bank of the inland sea, Israel's main source of fresh water.
Barak was also willing to offer the Syrians land to compensate for the small swath on the northeastern shore that he wanted to keep, Yatom told Army Radio.
To get the Israeli message across, Labour Party lawmaker Yatom approached Arab Knesset member Azmi Bishara in a meeting in the parliamentary cafeteria and sketched the Israeli position on a napkin.
"[Yatom] tried to say that Israel wants only symbolic control of the shore, in some places just 10 metres, sometimes 200 metres," Bishara said.
"He [Yatom] said they would compensate Syria by giving it land not under Syrian control in 67... He drew this on a napkin."
Bishara called journalists to say that he had talked to Syrian officials about many ideas, including the Israeli government positions - but had not acted as a messenger.
Talks between Barak and then-Syrian President Hafidh al-Asad collapsed, with Israel refusing to commit to allowing Syria a foothold on the shore of the Sea of Galilee.
Israel wanted "only symbolic control of the shore, in some places just 10 metres, sometimes 200 metres"
Arab Knesset member
Syria also refused to spell out the extent of the peace unless it received the Israeli commitment first.
In a newspaper interview last month, current Syrian President Bashar al-Asad called on Israel to renew talks. Syria had said several times since then that the talks would have to resume from the point where they stopped, but Israel had rejected that.
Israel's current hard-line government opposes withdrawing from the Golan Heights, a strategic plateau overlooking northern Israel, even for peace with Syria.
Start from scratch
Israeli Prime Minister Ariel Sharon has said he welcomes renewed peace negotiations with Syria, but they must start from scratch.
Israel captured the Golan Heights from Syria in the 1967 war, and Syria wants a complete Israeli withdrawal from the strategic plateau to the eastern waterline of the Sea of Galilee, in exchange for peace.
Bishara said the meetings took place in the period between an unsuccessful Israeli-Syrian meeting in Washington in December 1999, and a final meeting between US President Bill Clinton, who was mediating, and Hafidh al-Asad in March 2000.
No progress was made and the talks collapsed.