Senior US and Israeli officials all suggested an agreement was close last Sunday, although observers have cautioned that any potential deal could easily collapse.
Michael Herzog, the Israeli ambassador to Washington, said Israel hoped a significant number of hostages could be released.
Qatar has been at the centre of mediation efforts to reach an agreement that would lead to the release of hostages.
Sheikh Mohammed bin Abdulrahman Al Thani, the Qatari prime minister, at a press conference in Doha with Josep Borrell, the EU's foreign policy chief, said: "The challenges facing the agreement are just practical and logistical."
The White House deputy national security adviser, Jon Finer, said any agreement to free "considerably more than 12" hostages would be likely to also include an extended pause in the fighting and allow for the distribution of humanitarian assistance in Gaza.
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