Israeli officials have approved the US proposal for a temporary ceasefire in the nearly 20-month war.
US President Donald Trump has said negotiators were nearing a deal.
"There are some notes and amendments to some points, especially on the US guarantees, the timing of hostage release, the delivery of aid and the withdrawal of Israeli forces," the official said, speaking on condition of anonymity due to the sensitivity of the talks.
A separate Hamas statement said the proposal aims for a permanent ceasefire, a comprehensive Israeli withdrawal from Gaza and an ensured flow of aid.
It said 10 living hostages and the bodies of 18 others would be released " in exchange for an agreed-upon number of Palestinian prisoners".
A ceasefire would pause the fighting for 60 days, release some of the 58 hostages still held in Gaza in exchange for Palestinian prisoners and much-needed food aid and other assistance, according to Hamas and Egyptian officials who spoke on condition of anonymity because they were not authorised to talk to the media.
As hopes for a ceasefire ramp up, desperation rises inside Gaza.
Palestinians in the Gaza Strip blocked and offloaded dozens of food trucks, the UN World Food Program says, as desperation mounts following Israel's months-long aid blockade while talks of a ceasefire inch forward.
The World Food Program said 77 trucks carrying aid, mostly flour, were stopped by hungry people who took the food before the trucks could reach their destination.
The nearly three-month Israeli aid blockade on Gaza has pushed the population of over two million to the brink of famine.
The World Food Program said the fear of starvation in Gaza is high despite the aid that's entering now.
"We need to flood communities with food for the next few days to calm anxieties and rebuild the trust with communities that more food is coming," it said in a statement, adding that it has over 140,000 metric tons of food, enough to feed Gazans for two months, ready to be brought in.
A witness in the southern city of Khan Younis told The Associated Press the UN convoy was stopped at a makeshift roadblock and offloaded by desperate civilians in their thousands.
Most people carried bags of flour.
He said at one point a forklift was used to offload pallets.
The UN says it has been unable to get enough aid in because of fighting.
A new US and Israeli-backed foundation started operations in Gaza this week, distributing food at several sites in a chaotic rollout.
Israel says the Gaza Humanitarian Foundation eventually will replace the aid operation that the UN and others have carried out during nearly 20 months of war.
It says the new mechanism is necessary, accusing Hamas of siphoning off large amounts of aid.
The UN denies that a significant diversion takes place.
The Gaza Humanitarian Foundation works with armed contractors, which it says are needed to distribute food safely.
Aid groups have accused the foundation of militarising aid.
Israel continued its military campaign across Gaza, saying it struck dozens of targets over the past day.
Gaza's Health Ministry said at least 60 people were killed by Israeli strikes in the past 24 hours.
The war began when Hamas attacked Israel on October 7, 2023, killing around 1200 people, most of them civilians, and taking 250 hostages. Of those taken captive, 58 remain in Gaza.
Israel believes 35 are dead and Prime Minister Benjamin Netanyahu has said there are doubts about the fate of several others.
Israeli strikes have killed more than 54,000 Gaza residents, mostly women and children, according to Gaza's Health Ministry, which does not distinguish between civilians and combatants in its tally.
