The implications of a deal would be enormous. It would end the state of war that has lasted since 1947, pave the way for a final treaty with Lebanon, Syria's client state, and provide Israel with peace on all its frontiers for the first time.
It is for these reasons that Syria's President, Hafez al-Assad, has negotiated so tenaciously for his land and Israel's Prime Minister, Yitzhak Rabin, has played his own hand with such caution. To radical Arab nationalists and Jewish settlers alike, a compromise would constitute the ultimate betrayal. Intransigence on the part of the Israeli or Syrian leaderships could still make it impossible.
But there is evidence that the possibility of peace is real. It comes from the secretive Syrian leader himself. President Assad may not yet have crossed the River Jordan, but he certainly seems to have crossed the Rubicon.
An analysis of President Assad's rare public pronouncements reveals how far Syria has moved from the days when Israel was referred to as an illegal "entity", and great victories were declared to be imminent.
For some months, Syria's obedient media has talked of "full withdrawal in return for full peace", preparing the public for peace with the enemy in exchange for the recovery of the Golan Heights, which were lost to Israel in the Six Day War of 1967, when President Assad was defence minister.
On 1 June, President Assad laid to rest on television official Syrian mythology. He said that Syria was committed to regaining its border before 1967 and on this there would be no room for compromise. But he referred to "Israel" by name and he told Syrian viewers how high was the status of the negotiations.
"There is a US mediator who comes to us and meets me. He then goes to the other party and meets the head of the other side. Neither we nor they has a level higher than this," Mr Assad said.
This signified that he was taking personal responsibility for the talks, which had been hitherto left to lower-ranking officials.
Most extraordinary of all to an Arab audience was President Assad's public abandonment of his demand for a unified Arab position and his acknowledgement that Syria could no longer condemn Arab countries who made the vilified "separate peace" with the Zionist enemy.
"We earlier pledged that we would not advance a single step until others advanced as well," the President told his people. "But what can we do, since the others have left us and gone forward? They say they have made it ahead of us. We do not want anyone to go backward."
Israeli analysts have long believed that President Assad has made a "strategic decision" for peace. Now he seems to have moved faster in public than many expected, and the response from Israel has been swift.
The Israeli Foreign Minister, Shimon Peres, said on 5 June that "the Golan Heights were never historically part of Israel". It was "a historical fact" that they belonged to Syria.
Yesterday, Israel's President, Ezer Weizmann, confirmed for the first time that the Israeli government was considering "a withdrawal to the international border".