Earlier this week Israel's seven-member security cabinet held a series of intensive meetings to discuss the issue.
On Wednesday Eli Yishai, the Israeli security minister, reiterated his misgivings over a prisoner amnesty that could boost Hamas.
"We always say 'not at any price' because otherwise our enemies would exploit it. But on the other hand, we have to make every possible effort," Yishai told Israel's Army Radio.
"Where is the middle ground? I think any further (public) words about this would be excessive."
Speaking to Reuters Fawzi Barhoum, a Hamas spokesman in Gaza, said the group had received Israel's proposal and "will study the response".
Another unnamed Hamas official said the group planned to send a delegation from Gaza Damascus by Thursday to meet exiled Hamas leaders for a "broader discussion" on any possible prisoner exchange.
Under the proposed swap about 1,000 of the some 11,000 Palestinians held in Israeli prisons would be released.
However, Reuters quoted officials familiar with the negotiations as saying Israel had ruled out releasing a handful of senior Hamas fighters serving life sentences for orchestrating lethal attacks against Israelis.
Binyamin Netanyahu, the Israeli prime minister, is also thought to be was also intent on barring between 100 and 120 other Palestinians from returning to the West Bank, saying they should be sent instead to Gaza or into exile abroad.