Israel’s war cabinet could approve a US plan for a ceasefire with Hezbollah in Lebanon on Tuesday.
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, Israeli media reported.
White House national security spokesperson John Kirby said on Monday, “We're close" but "nothing is done until everything is done".
The French presidency said discussions on a ceasefire had made significant progress.
Mr Netanyahu's office declined on Monday to comment on reports that Israel and Lebanon had agreed to the text of a deal.
Hezbollah, a designated terror group in the West, has endorsed its ally Lebanese Parliament Speaker Nabih Berri to negotiate.
The plan requires Israeli troops to withdraw from south Lebanon and Lebanese army troops to deploy in the border region - a Hezbollah stronghold - within 60 days, Elias Bou Saab, Lebanon's deputy parliament speaker, said.
Signs of a breakthrough have been accompanied by military escalation, with Israeli airstrikes demolishing more of Beirut's Hezbollah-controlled southern suburbs on Monday.
In Israel, a ceasefire will pave the way for 60,000 people to return to homes in the north, which they evacuated as Hezbollah began firing rockets in support of its Palestinian ally Hamas a day after Hamas launched its terror attack on Israel.
Israel has dealt Hezbollah massive blows since going on the offensive against the group in September, killing its leader Sayyed Hassan Nasrallah and other top commanders.
The group has kept up rocket fire into Israel, firing some 250 rockets on Sunday.
Israel's ambassador to the United Nations, Danny Danon, said on Monday that Israel would maintain an ability to strike southern Lebanon under any agreement.
Lebanon has previously objected to Israel being granted such a right, and Lebanese officials have said such language is not included in the draft proposal.
The US State Department said on Monday gaps between the two parties have narrowed significantly but there are still steps they need to take to reach an agreement.
"Oftentimes the very last stages of an agreement are the most difficult because the hardest issues are left to the end," a spokesperson said. "We are pushing as hard as we can."
In Beirut, Bou Saab told Reuters on Monday there were "no serious obstacles" left to start implementing a U.S.-proposed ceasefire with Israel, "unless Netanyahu changes his mind".
Over the past year, more than 3,750 people have been killed and over one million have been forced from their homes, according to Lebanon's health ministry, which does not distinguish between civilians and combatants in its figures.
Hezbollah strikes have killed 45 civilians in northern Israel and the Israeli-occupied Golan Heights.
At least 73 Israeli soldiers have been killed in northern Israel, the Golan Heights and in combat in southern Lebanon, according to Israeli authorities.
