The comments came as Axios reported that Israeli and Qatari officials met late on Friday in an effort to revive talks.
The Egyptian sources said Israeli officials appeared to have changed their mind on some points that they had previously refused, but did not go into further detail.
Israeli Prime Minister Benjamin Netanyahu appeared to hint that new negotiations were under way to recover hostages held by Hamas, after Israeli and Qatari officials held talks.
In a news conference, Netanyahu said Israel's offensive in Gaza helped clinch a partial hostage-release deal in November. "The instruction I am giving the negotiating team is predicated on this pressure, without which we have nothing," he said.
Israeli occupation forces bombarded targets across Gaza yesterday including a crowded YMCA building, with dozens of Palestinians reported killed or wounded.
The territory's Hamas government says the war has killed at least 18,800 people, mostly women and children.
Two Christian women who had taken refuge in a church complex in Gaza were shot dead by an Israeli soldier, Catholic Church authorities said.
In Khan Younis in Gaza's south, Palestinian health officials said the Nasser Hospital had received 20 Palestinians killed in air strikes overnight, in addition to dozens of wounded, including women and children.
Palestinian health officials also said Israeli strikes on Gaza City in the north had hit the YMCA headquarters, which is sheltering hundreds of displaced people and reported several dead and wounded.
