Hariri was expected to be nominated by members of his parliamentary majority coalition, which defeated the Syrian-Iranian backed Hezbollah-led opposition in the June parliamentary election.
Hariri was appointed after the elections as premier, but he stepped down last week after failing to reach an agreement with the opposition to form a national unity government.
Political observers blamed the failure to form a national unity government on regional issues and the souring of ties between Saudi Arabia and Syria.
Saudi Arabia is a main supporter of the Western-backed majority, while Syria and Iran strongly support the Hezbollah led-opposition.
Under the Lebanese constitution, the prime minister should be a Sunni Muslim, the House Speaker a Shia, and the president a Christian.