Thirty-three hostages, living and dead, are expected to be freed in the first phase of the ceasefire deal, according to a person with direct knowledge of the ongoing negotiations.
There are 94 abductees remaining in Gaza, including 34 who have been confirmed dead, according to Israeli officials.
-ABC News' Jordana Miller
A source close to the ongoing Gaza ceasefire talks in Qatar told ABC News that Israel is waiting for Hamas to approve moving into a final "closing round of negotiations," adding there is a "real chance" for a "breakthrough" after a diplomatic blitz in Doha this weekend.
"We still have ahead of us a closing round of negotiations," the source added
Reuters reported Monday that mediators in Qatar handed both Israel and Hamas a final draft of the ceasefire proposal, citing an official briefed on the negotiations.
Reuters reported that the official said a breakthrough was reached after talks between Steve Witkoff -- President-elect Donald Trump's Middle East envoy -- the Qatari prime minister and Israeli spy chiefs.
Israeli Foreign Minister Gideon Saar, meanwhile, said Monday "there is progress," and that the situation "looks much better than previously."
"I don't want to say more than that because I realize there are families and they are sensitive to every word, and every sentence," Saar added. "I hope that within a short time we will see things happening, but it is still to be proved."
-ABC News' Jordana Miller and Guy Davies
Israel's far-right Finance Minister Bezalel Smotrich said he will not support the potential Gaza ceasefire deal currently being negotiated in Qatar, describing it as "a catastrophe for the national security of Israel."
"We will not be part of a surrender deal that would include releasing arch terrorists, stopping the war and destroying its achievements that were bought with much blood and abandoning many hostages," Smotrich wrote in a post to X on Monday.
"Now is the time to continue with all our might, to occupy and cleanse the entire strip, to finally take control of humanitarian aid from Hamas and to open the gates of hell on Gaza until Hamas surrenders completely and all the hostages are returned."
-ABC News' Dana Savir
Israeli Prime Minister Benjamin Netanyahu's office said he spoke with President Joe Biden on Sunday about progress in negotiating a ceasefire and hostage deal.
A senior White House administration official confirmed the call to ABC News.
"The Prime Minister discussed with the US President the progress in negotiations for the release of our hostages, and updated him on the mandate he gave to the negotiating delegation to Doha, in order to promote the release of our hostages," Netanyahu's office wrote in a release about the call.
According to the White House, Biden and Netanyahu "discussed the fundamentally changed regional circumstances following the ceasefire deal in Lebanon, the fall of the Assad regime in Syria, and the weakening of Iran’s power in the region."
The call comes as Brett McGurk, the White House Coordinator for the Middle East and North Africa, is in the Middle East for negotiations. National Security Adviser Jake Sullivan told CNN's "State of the Union" on Sunday that McGurk is there to hammer out the "final details" of an agreement.
-ABC News' Jordana Miller and Michelle Stoddart