Two leading Israeli cabinet ministers have said Israel should respond to a Syrian offer of peace negotiations.
Israel captured the Golan Heights from Syria in 1967
Ex-prime minister Binyamin Netanyahu said Syria was in a difficult position after the overthrow of Saddam Hussein, and Israel could win the negotiations.
Foreign Minister Silvan Shalom said Syria's offer should not be ignored.
Last month, Syrian President Bashar al-Assad said he was ready to resume negotiations with Israel where they left off in the year 2000.
That would mean Israel withdrawing from nearly all of the Golan Heights, which were captured from Syria in 1967, says the BBC's Chris Morris in Jerusalem.
"Bearing in mind Syria's very precarious position, it's in our interest to exploit recent overtures for contacts," Mr Netanyahu told Israel radio.
"Syria is in a very troubled situation, with a dictatorial government that is struggling to survive, confronted by a great historical change [in Iraq],» he said.
"They need a peace agreement with us like the air that they breathe ... a lot more than we do."
And he suggested that this could mean there was a change to reach an agreement "without withdrawing from the Golan."
Netanyahu remains an influential figure in Israel
Mr Shalom said the Israeli Government should examine "seriously Syria's intentions".
Mr Assad's apparent willingness to talk has divided Israeli political circles.
Security sources in Israel say some of the most senior officials in the Israeli military agree.
But Defence Minister Shaul Mofaz has said he does not think Syria is serious, and Prime Minister Ariel Sharon has shown little interest in the proposal so far.
"If Syria's intentions are serious, they should dismantle [the militant group] Hezbollah and stop their support for Palestinian terror and disband the commands in Damascus. Only then will it be possible to think about negotiations."
The Middle East is awash with diplomatic initiatives, says the BBC's Paul Wood in Jerusalem.
Libya is talking to Israel. Egypt is talking to Iran. Turkey is passing messages from Israel to Syria. In fact, almost the only people who are not talking to one another are Israel and the Palestinians, our correspondent says.
On Wednesday, it was leaked that Israeli and Libyan officials had been in contact to explore ways of establishing diplomatic relations - alarming both sides.
A day later, Mr Shalom said Israel would be ready to open talks with Tripoli "if Libya changes its attitude towards Israel and stops backing terrorism and destroys its weapons of mass destruction".
Ephraim Halevy, former head of Israel's secret service Mossad, says the Middle East could undergo a more radical transformation now than during the early part of the 20th Century, when the great powers redrew the map.
And there is certainly genuine excitement in Israel following initial contacts with Libya - denied by Tripoli - our correspondent says.
The Israeli prime minister's office has been playing down expectations that normal ties can be restored easily.
But there is no doubt the strategic situation has been transformed in the Middle East, our correspondent says.
The question is whether that will alter the sad dynamic of the Israeli-Palestinian conflict after more than three years of bloodshed, he says.