A Palestinian official, speaking on condition of anonymity, told Reuters that Egypt also put forward a bridging proposal, but Hamas had yet to respond.
The official declined to provide details of the plan, which he said was under consideration.
Two Egyptian security sources said Egypt had suggested setting a timeline for the release of the remaining hostages alongside a deadline for a full Israeli pullout from Gaza with US guarantees.
The sources said the US had signaled initial approval, while Hamas' and Israel's responses were expected later on Friday.
Egypt could take in Gazans
The report of Egypt's proposal comes after Hamas said it was still debating US special envoy Steve Witkoff's proposal and other ideas, with the goal of reaching a deal on prisoner releases, ending the war, and securing a complete Israeli military withdrawal from the Gaza Strip.
Additionally, Hezbollah-affiliated Lebanese newspaper Al-Akhbar reported on Friday that Egyptian President Abdel Fattah El-Sisi signaled that his country would be willing to take in half a million Gazans on temporary terms.
The report came after Sisi attended an Arab conference in Riyadh, Saudi Arabia. Al-Akhbar reported that Gazans would be moved to a city in the North of the Sinai Peninsula.
Earlier this year, US President Donald Trump said that he thought Egypt and Jordan should take in displaced Palestinians while the Gaza Strip is rebuilt.
Trump, in an apparent reference to Egypt and Jordan, said in February that the US does "a lot for them, and they are going to do it."
Jerusalem Post Staff contributed to this report.