That optimism was shared by Lebanese Foreign Minister Abdallah Bou Habib who expressed hope at a G7 meeting in Italy that a ceasefire would be reached by Tuesday night.
Israel's security cabinet is expected to convene later on Tuesday to discuss and likely approve the text at a meeting chaired by Prime Minister Benjamin Netanyahu, the official said.
This would pave the way for a ceasefire declaration by US President Joe Biden and French President Emmanuel Macron, four senior Lebanese sources told Reuters.
In Washington, White House national security spokesperson John Kirby said, "We're close" but "nothing is done until everything is done".
The French presidency said discussions on a ceasefire had made significant progress.
A ceasefire between Hezbollah and Israel will reportedly be announced by Biden and Macron. (AP PHOTO)
The agreement requires Israeli troops to withdraw from south Lebanon and Lebanon's army to deploy in the region - a Hezbollah stronghold - within 60 days, officials say. Hezbollah would end its armed presence along the border south of the Litani River.
Israel demands effective UN enforcement of an eventual ceasefire with Lebanon and will show "zero tolerance" toward any infraction, Defence Minister Israel Katz said on Tuesday.
Netanyahu's office declined to comment on reports that both Israel and Lebanon had agreed to the text of a deal.
Israeli officials had said earlier that a deal to end the war was getting closer though some issues remained, while two senior Lebanese officials voiced guarded optimism even as Israel continued to bombard Lebanon and Hezbollah kept up rocket fire.
Israel's ambassador to the United Nations, Danny Danon, said Israel would maintain an ability to strike southern Lebanon under any agreement. Lebanon has previously objected to wording that would grant Israel such a right.
The United States has pushed for a deal between Iran-backed Hezbollah and Israel to end the fighting that erupted in October, 2023 in parallel with Israel's war against Palestinian Islamist group Hamas in Gaza. The conflict in Lebanon has drastically escalated over the last two months.
In Beirut, Elias Bou Saab, Lebanon's deputy parliament speaker, told Reuters there were "no serious obstacles" left to start implementing a US-proposed ceasefire with Israel, "unless Netanyahu changes his mind".
He said the proposal would entail an Israeli military withdrawal from south Lebanon and regular Lebanese army troops deploying in the border region, long a Hezbollah stronghold, within 60 days.
A sticking point over who would monitor compliance with the ceasefire had been resolved in the past 24 hours with an agreement to set up a five-country committee, including France and chaired by the US, he said.
Hostilities have intensified despite diplomatic progress. Over the weekend, Israel carried out powerful air strikes, one of which killed at least 29 people in central Beirut, while Hezbollah unleashed one of its biggest rocket salvos yet on Sunday, firing 250 missiles into Israel.
A photo of slain Hezbollah leader Hassan Nasrallah hangs in a destroyed building in Beirut, Lebanon. (AP PHOTO)
In Beirut, Israeli air strikes levelled more of the Hezbollah-controlled southern suburbs on Monday, sending clouds of debris billowing over the Lebanese capital.
Efforts to clinch a truce appeared to advance last week when US mediator Amos Hochstein declared significant progress at talks in Beirut, then held meetings in Israel.
Israel has dealt major blows to Hezbollah, killing its leader Hassan Nasrallah and other top commanders, and inflicting massive destruction in areas of Lebanon where the group holds sway.
Israel says it had no choice but to launch its military campaign so tens of thousands of Israelis could return to homes they were forced to evacuate when Hezbollah began firing across the Lebanese border into Israel more than a year ago. Hezbollah's campaign followed the Hamas-led October 7, 2023, attacks on Israel that precipitated the Gaza war.
Lebanon's health ministry said Israeli attacks have killed 3768 people in Lebanon and forced more than one million people from their homes. Its casualty figures do not distinguish between civilians and combatants.
