"I hope that they will decide today," Aviva Shalit, the soldier's mother had said. "And that each minister knows that his decision will decide whether Gilad lives or dies."
Following the meeting with the prime minister, Noam Shalit, the soldier's father, said: "I am not pessimistic but nor am I optimistic."
At a protest outside the prime minister's official residence, dozens of demonstrators carried cardboard cutouts of Shalit and urged the cabinet ministers to wrap up an agreement.
If approved, the exchange would be subject to a 48-hour period for opponents to file legal challenges.
There was no immediate comment on a potential exchange from Hamas officials, but there has been increasing anticipation of a deal being reached in recent weeks.Negotiations
Intermittent negotiations between Israel and Hamas have been conducted indirectly, mainly through Egypt, since Shalit was seized by fighters from Hamas and allied groups.
|Shalit was seized in a cross-border raid by Palestinian fighters in 2006 [AFP]
On Sunday, Omar Suleiman, Egypt's intelligence chief, held the latest in a series of talks with senior officials in Israel.
Germany, which has a history of organising successful prisoner exchange between Israel and Lebanon's Hezbollah, has also been involved in mediating in recent months.
Israel has, so far, been reluctant to meet Hamas's demand for the release of dozens of Palestinians convicted of carrying out deadly attacks on Israelis.
It also wants Hamas to agree to some of the prisoners being deported to areas other than the West Bank to prevent them from joining groups of Palestinian fighters in the future.
The Associated Press news agency quoted a Palestinian source as saying that the Palestinian prisoners would be released in two stages.
A first group of 450 are to be freed as Shalit is handed over to the Egyptians, and then returned to Israel. The remainder would be released weeks or even months later.
More than 10,000 Palestinians are currently being held in Israeli jails.
In October, Israel freed about 20 Palestinian women prisoners in exchange for a video showing Shalit in captivity.
The video showed Shalit alive and moving - the first proof of his wellbeing since he was captured.