The United States, European Union and United Nations have pushed in recent days for a truce in the long-running hostilities between Israel and Hezbollah, which escalated into full-scale war in late September.
As truce talks intensified, Lebanon's health ministry said Israeli strikes killed at least 31 people on Monday, mostly in the south.
An Israeli official, speaking on condition of anonymity, said the security cabinet "will decide on Tuesday evening on the ceasefire deal".
US National Security Council spokesman John Kirby said the talks were progressing but not finalised.
"We believe we've reached this point where we're close," he said, adding "we're not there yet".
While Israel presses its offensive on Palestinian militants Hamas in Gaza, the United States and France have led efforts to broker a ceasefire in Lebanon, where Israel is battling the Iran-backed Hezbollah on a second front.
France reported "significant progress" in ceasefire talks, and Italy, which holds the rotating presidency of the G7 group of nations, expressed "optimism" over a truce in Lebanon.
US news outlet Axios reported the draft agreement includes a 60-day transition period.
Israeli forces would withdraw, the Lebanese army would redeploy near the border, and Hezbollah would move heavy weapons north of the Litani River, said Axios.
A US-led committee would oversee implementation, with provisions allowing Israel to act against imminent threats if Lebanese forces fail to intervene, it added.
News of the security cabinet meeting came as the Israeli military said it carried out a wave of strikes on Monday, including on Beirut's southern suburbs, a Hezbollah stronghold that Israel has repeatedly bombed since late September when it escalated its air campaign in Lebanon.
The latest strikes hit around two dozen Hezbollah targets across Lebanon in one hour, the military said. A statement said "command centres, and intelligence control and collection centres, where Hezbollah commanders and operatives were located", were targeted.
The strikes followed intense Hezbollah fire over the weekend, including some attacks deep into Israel.
Syria strikes
Israeli media reported that Prime Minister Benjamin Netanyahu was likely to endorse the US ceasefire proposal.
Asked in New York about the possible truce agreement, Israel's UN ambassador Danny Danon said "we are moving forward on this front", adding the cabinet would meet to discuss it.
The war in Lebanon followed nearly a year of limited cross-border exchanges of fire initiated by Hezbollah. The Lebanese group said it was acting in support of Hamas after the Palestinian group's October 7, 2023 attack on Israel, which sparked the war in Gaza.
Lebanon says at least 3,768 people have been killed in the country since October 2023, most of them in the past few weeks.
On the Israeli side, the Lebanon hostilities have killed at least 82 soldiers and 47 civilians, authorities say.
Deal a 'mistake'
The initial exchanges of fire forced tens of thousands of Israelis to flee their homes, and Israeli officials have said they are fighting so the residents can return safely.
Some northern residents expressed fears as to whether that was possible under a ceasefire.
"In my opinion, it would be a serious mistake to sign an agreement as long as Hezbollah has not been completely eliminated," said Maryam Younnes, 29, a student from Maalot-Tarshiha.
"It would be a mistake to sign an agreement as long as Hezbollah still has weapons."
Dorit Sison, a 51-year-old teacher displaced from Shlomi, said: "I don't want a ceasefire, because if they do it along the lines that they've announced, we'll be in the same place in five years."
Israel's far-right National Security Minister Itamar Ben Gvir warned on X that reaching a Lebanon ceasefire deal would be a "historic missed opportunity to eradicate Hezbollah".
Ben Gvir has repeatedly threatened to bring down the government if it agrees to a truce deal with Hamas in the Gaza Strip or Hezbollah in Lebanon.
Efforts this year by mediators to secure a truce and hostage-release deal in the Gaza war have failed.
Qatar early this month said it was suspending its mediation role until the warring sides showed "seriousness".
With an intensive Israeli military operation in besieged north Gaza continuing, remaining residents were left "scavenging among the rubble" for food, said Louise Wateridge, spokeswoman for the UN agency for Palestinian refugees, UNRWA.
Such scavenging puts Gazans at risk of encountering unexploded and unused ordnance that can be found in many populated areas of the territory, the Danish Refugee Council said.
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