Hamas's leader Ismail Haniyeh says they are "close to reaching a truce agreement".
There has been no update from Israel.
The deal could see Hamas returning hostages in exchange for Israel's release of jailed Palestinians, according to AFP and Al Jazeera.
US President Joe Biden had earlier indicated a deal could soon be agreed that would involve Hamas releasing hostages from Gaza in exchange for pauses in fighting.
The International Committee of the Red Cross, which helped facilitate previous deals, has further raised hopes by saying its head is meeting Hamas.
The head of Gaza's Indonesian Hospital has told the BBC that "intermittent shooting" is still being heard at the site, where 500 patients remain inside.
Gaza's Hamas-run health ministry says 13,300 people have been killed in the territory since Israel started its campaign.
Israel began attacking Gaza after Hamas fighters crossed the border on 7 October and went on to kill 1,200 Israelis while taking more than 200 others hostage.
