Israel and Syria, bitter enemies, have recently renewed indirect discussions, with Turkish-mediation. Olmert, in an interview with France's Le Figaro newspaper, was quoted as saying that direct talks could be opened once Israel and Syria agree on a precise agenda and issues to discuss.
"We aren't far away," Olmert was quoted as saying. "If the two parties are serious, we should soon sit down at a table for talks."
Both Olmert and Syrian President Bashar Assad are expected to participate in a Paris summit on July 13.
Claude Gueant, French President Nicolas Sarkozy's chief of staff, told Europe-1 radio that Olmert recommended the two leaders hold "direct contacts" during the Paris summit.
Later Wednesday, another official in Sarkozy's office said such a meeting was not expected, as talks were not at that point yet. The official spoke on condition that his name not be used, because of office policy.
Olmert, asked about a potential meeting with Assad in Paris, sidestepped the question: "Sarkozy 'knows better than me what will happen in Paris," he was quoted as telling Le Figaro.
Previous peace talks between Israel and Syria broke down in 2000. Indirect contacts have been going on for months, but no results have been made public.
Olmert said that better relations with Syria would alter the whole dynamic of the Middle East.
"If there's an Israeli embassy in Damascus, things will change," he was quoted as saying. "It will also make a difference in Lebanon. If we negotiate with Syria, why not with Lebanese Prime Minister Fuad Saniora?"
Last week, when Olmert hinted Israel would be interested in talks with Beirut, the Lebanese government rejected them. On Wednesday, a Lebanese government official said that position hadn't changed.