People look at pictures of Hamas' hostages during a demonstration in Tel Aviv, Israel, calling for their release on November 11.
CNN  — 

A recent draft of a possible deal to secure the release of hostages that Hamas is holding in Gaza proposes a four- to five-day pause in fighting for the initial release of 50 hostages, two sources familiar with the talks told CNN.

An agreement has yet to be struck and the text of a deal has been traded back and forth for weeks. But negotiators from various countries, including senior Biden administration officials, are expressing rare optimism about the progress. Gaps in some of the major sticking points have begun to close, sources say, and while the talks could still break down, an agreement may now be days away.

“We think that we are closer than we have been perhaps at any point since these negotiations began weeks ago,” deputy national security adviser Jon Finer told CNN’s Jake Tapper on “State of the Union” on Sunday. Finer did not get into details of the talks and stressed that there is no final deal in place.

In a sign of how tenuous the talks have been, two sources told CNN that in recent days, Hamas had put the negotiations on hold at least once. One of the many issues that the terrorist group raised, and that appeared to have prompted Hamas abruptly going dark amid the talks, was Israel’s raid of Al-Shifa hospital in Gaza. But the discussions eventually picked back up.

One key issue yet to be finalized is how to implement the deal, including around aid shipments to Gaza, one source familiar with the negotiations said Sunday on the heels of a meeting between Qatar’s prime minister and Brett McGurk, the White House coordinator for Middle East affairs. Qatar has served as a main interlocutor in the talks.

The most recent discussions have proposed the staggered release of civilian hostages, with pauses potentially increasing after Hamas allows for an initial release of a significant number of those captured, according to the sources.

Israel has presented a list of approximately 100 civilian hostages it wants included in the agreement, one source told CNN. Israel has publicly demanded that all hostages be released. Hamas indicated it would be willing to release 50 hostages over a multiday pause. More hostages, around 20 to 25, could be released after that as the pauses are extended.

Hamas has said it needs pauses in fighting to gather the hostages who are being held in different places and by different Hamas-allied groups in Gaza.

The National Security Council and the Israeli embassy to the US declined to comment for this story. The Qatari Embassy to the US didn’t respond immediately to a request for comment.

There are still details to be worked out over aid, with Israel expressing concern that aid could go to help Hamas rather than civilians. Hamas initially requested 500 trucks of aid per day, one of the sources said. One source said no agreement has been reached on how many aid trucks could enter Gaza but that more than 200 trucks was logistically challenging.

There are also questions about how to inspect the trucks and which points of entry would be used. The aid, including fuel and cooking oil for bakeries, would continue to flow in after the initial pauses for hostages.

CNN’s Priscilla Alvarez contributed to this report.