Safadi, 75, is a prominent businessman and former member of parliament from the predominantly Sunni city of Tripoli
Three major Lebanese parties agreed to nominate Mohammad Safadi, a former finance minister, to become prime minister, three sources familiar with the situation said, suggesting progress towards a new government at a time of acute economic crisis.
Saad al-Hariri quit as prime minister on October 29 in the face of an unprecedented wave of protests against ruling politicians who are blamed for rampant state corruption and steering Lebanon into its worst economic crisis since the 1975-90 civil war.
The consensus on Safadi emerged in a meeting late on Thursday between Hariri, a leading Sunni politician aligned with Western and Gulf states, and representatives of the Iran-backed Shi'ite group Hezbollah and its Shi'ite ally Amal.
The news was first reported by Lebanese broadcasters LBCI and MTV.
A source familiar with the meeting said Hariri had expressed no objections to Safadi's nomination, adding that MPs from Hariri's Future Movement would nominate Safadi in a formal process expected to begin soon.
A second source, a senior figure close to Amal and Hezbollah, said agreement in principle on Safadi's nomination had emerged at the meeting.
There was no official confirmation from the parties or Safadi.
Safadi, 75, is a prominent businessman and former member of parliament from the predominantly Sunni city of Tripoli. He previously served as finance minister and minister of economy and trade.
Lebanon's prime minister must be a Sunni Muslim, according to its sectarian power-sharing system.
The next government will face huge challenges.
It must win international financial support seen as critical to alleviating the economic crisis while addressing the challenge posed by a nationwide protest movement that wants to see the old elite gone from power.
Lebanon's long-brewing economic crisis, rooted in years of state waste, corruption and mismanagement, has deepened since the protests began. Banks have imposed controls on transfers abroad and US dollar withdrawals.
Served under Mikati, Siniora
Hariri had said he would only return as prime minister of a Cabinet of specialist ministers that he believed would be best placed to win aid and save Lebanon from the crisis. To that end, he has been holding many closed-door meetings with other parties.
But while Hezbollah and Amal wanted Hariri to return as premier, the Shi'ite groups and President Michel Aoun, a Hezbollah ally, have been insisting that the Cabinet include both technocrats and politicians.
Listed as a terrorist group by the United States, the heavily armed Hezbollah and groups politically aligned with it hold a majority of seats in parliament.
The process requires Aoun, a Maronite Christian, to formally consult MPs on their choice for prime minister. He must designate whoever gets the most votes.
Hariri remains caretaker prime minister for now.
Safadi was finance minister from 2011 to 2014 under Prime Minister Najib Mikati.
In 2008, he became minister of economy and trade in the government of Western-backed Prime Minister Fouad Siniora. He held that post again in a Hariri-led Cabinet formed in 2009.
Safadi was part of the Hariri-led "March 14" alliance that emerged after the 2005 assassination of Rafik al-Hariri, Saad's father. March 14 mobilised against the presence of Syrian forces that withdrew from Lebanon in 2005 and was then locked in years of political conflict with Hezbollah over its weapons.
A 2009 US Embassy cable published by WikiLeaks described Safadi as having made his fortune in Saudi Arabia and being close to the Saudi royal family.
He was first elected as an MP in Tripoli in 2000 but did not stand in the last election.
His wife, Violette Safadi, is the minister of state for economic empowerment of women and youth in the Hariri cabinet.