"We expect the deal to move ahead, and it is possible we will have [Eldad] Regev and [Ehud] Goldwasser back in Israel next week," a senior Israeli government official in Jerusalem said.
Hezbollah captured Goldwasser and Regev, both army reservists, during a cross-border raid that triggered a war in 2006 between the group and Israel.
Olmert declared the two soldiers dead before his cabinet approved the deal, but Hassan Nasrallah, the secretary-general of Hezbollah, has not allowed aid agencies to visit the soldiers, and called the declaration "speculation".
An Israeli government statement said the completion of the deal still depended on a number of components being finalised, after which Olmert's cabinet would vote to give it final approval.
This includes a demand for further information on Ron Arad, a pilot who was captured alive after his aeroplane was shot down over Lebanon in 1986.
Hezbollah has compiled a report on Arad. Defence officials said an Israeli negotiator was in Europe on Monday to pick up the report.
However, Mark Regev, a spokesman for Olmert, said: "So far, we have not received the report concerning the fate of our missing navigator, Ron Arad.
"When that report is received, we will have discussions inside the government on how to move forward."
Nasrallah and Olmert had both signed the deal under which the Jewish state will release five Lebanese prisoners and Hezbollah will hand over two Israeli soldiers.
The Lebanese prisoners include Samir Kantar, the most prominent held by Israel. He is serving a life sentence for killing a police officer as well as a man and his four-year-old daughter during a 1979 raid on the northern coastal town of Nahariya.
On Monday, the family of the police officer appealed to Israel's supreme court to block the exchange.
"Don't release Kantar. He is a despicable mass murderer, and Israel will be sorry in the end," said Keren Shahar, the dead policeman's daughter.
Under the deal, which was negotiated by Gerhard Conard, a UN envoy, Israel will also hand over the bodies of about 200 Arab fighters killed while infiltrating northern Israel, while Hezbollah would return the body parts of Israeli soldiers killed in southern Lebanon in 2006.
The dead include Palestinian and Lebanese fighters killed in decades of conflict with Israel and the bodies of eight Hezbollah fighters.