Olmert said that he does not think talks will force Syria to break its links with Iran, the Lebanese Shia group, Hezbollah and the Palestinian Islamist organisation, Hamas.
Bashar al-Assad, the Syrian president, has called in recent months for a new round of talks with Israel.
"I don't think there is a Syrian desire for war with us. We certainly don't have a desire to fight with them. That doesn't mean conditions ripe for us to negotiate with them," Olmert said.
The report says that Israel should return the Golan Heights to Syria in return for a secure peace agreement.
"It does not make any sense to ease the US problem in Iraq by giving the Golan Heights to Syria"
Professor Tamar Rabinovich, Tel Aviv University
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Professor Tamar Rabinovich of Tel Aviv University told Al Jazeera that any US-Syria dialogue had to overcome a number a problems.
"It does not make any sense to ease the US problem in Iraq by giving the Golan Heights to Syria."
Rabinovich said that despite this, he was in favour of Israel holding exploratory talks with Syria.
Olmert, however, said that Israel was deeply interested in restarting new talks with the Palestinians and would work, "with all our might" to make them happen.
He also welcomed a peace initiative put forward by Saudi Arabia, saying it contains "interesting elements that should not be ignored."
However, he did not fully endorse the plan, which called for Israel to withdraw from all of the West Bank, Gaza and east Jerusalem, which Israel rejects.