A senior Hamas official told AFP the group would deliver its response to Israel's latest counterproposal for a Gaza ceasefire on Monday in Egypt.
"A Hamas delegation headed by Khalil al-Hayya will arrive in Egypt... and deliver the movement's response" to the Israeli proposal during a meeting with Egyptian intelligence officials, said the official who declined to be named.
Mediator Egypt sent its delegation to Israel last week to jump-start stalled negotiations even as fighting in the Gaza Strip rages.
Egypt, Qatar and the United States have been unsuccessfully trying to broker a new Gaza truce deal ever since a one-week halt to the fighting in November saw 80 Israeli hostages exchanged for 240 Palestinians held in Israeli prisons.
Diplomatic efforts have been stepped up in recent days to reach a truce and hostage-release deal.
US news website Axios, citing two Israeli officials, reported that Israel's latest proposal includes a willingness to discuss the "restoration of sustainable calm" in Gaza after hostages are released.
It is the first time in the nearly seven-month war that Israeli leaders have suggested they are open to discussing an end to the war, Axios said.
"Hamas is open to discussing the new proposal positively," another Hamas source close to the negotiations told AFP.
The source added that the group is "keen to reach an agreement that guarantees a permanent ceasefire, the free return of displaced people, an acceptable deal for (prisoner) exchange and ensuring an end to the (Gaza) siege".
The delegation would also discuss an Egyptian proposal concerning a ceasefire and prisoner exchange as part of the overall deal to stop the fighting in Gaza, the source said.
He said the Egyptian proposal showed "some progress".
It guarantees the absence of Israeli forces on Al-Rashid road, a key artery in the strip, when displaced Palestinians return from the south of the territory to the north, he said.
It also proposes that Israeli forces remain 500 metres away from the main Salaheddin highway and ensures that civilians are not subjected to shooting, arrest or detention when they return to their homes.
Al-Qahera News, which is linked to Egyptian intelligence services, reported "noticeable progress in bringing the views of the Egyptian and Israeli delegations closer".
Impasse
For several weeks now negotiations to end the war had hit an impasse.
In early April, Hamas had said it was studying a proposal, after talks in Cairo, and Al-Qahera reported progress. Days later Israel and Hamas accused each other of undermining negotiations.
Thousands of Israeli protesters meanwhile have stepped up pressure on Prime Minister Benjamin Netanyahu to strike a deal that would see the remaining hostages freed.
The Israeli army says 129 hostages are still held captive in Gaza, including 34 it says are dead.
Some 250 people were abducted by Palestinian militants when Hamas attacked Israel on October 7.
The attack resulted in the deaths of 1,170 people, Israeli and foreigners, according to an AFP tally based on official Israeli figures.
Israel's retaliatory military offensive in Gaza has killed 34,454 people, most of them women and children, according to the Hamas-run territory's health ministry.