The nomination, expected later in the day, sets the stage for the formation of a cabinet that excludes allies of the United States and Sunni Gulf Arab countries while underlining the influence of Iran's friends in Lebanon.
Diab, a little-known academic with a doctorate in computer engineering, has not commented publicly since his name surfaced overnight.
Lebanon, wrestling with the worst economic crisis since the 1975-90 civil war, has been in dire need of a new government since outgoing Prime Minister Saad al-Hariri resigned on Oct. 29, prompted by protests against the ruling elite.
But efforts to reach a deal on a new premier have been mired in divisions that reflect long-standing tensions between Hariri, who is aligned with Western and Gulf Arab states, and the heavily armed Shi'ite Muslim group Hezbollah. Washington regards Hezbollah as a terrorist group and has imposed sanctions on it.
President Michel Aoun, a Hezbollah ally who has also been at political loggerheads with Hariri, began consultations on Thursday with deputies to designate the new premier, who under the country's sectarian political system must be a Sunni Muslim.
Aoun, a Maronite Christian, is required to designate the candidate with the most support.
The move to nominate Diab signaled a decision by Hezbollah and its allies to abandon efforts to forge a consensus with Hariri and to install a candidate of their choosing, drawing on the parliamentary majority they secured in a 2018 election.
But it was not immediately clear how quickly a government would be formed. Until that happens, Hariri, Lebanon's leading Sunni politician, will stay on as caretaker prime minister.
CRISIS
Lebanon is facing an unprecedented financial crisis: banks are imposing tight capital controls, the Lebanese pound has slumped by a third from its official rate and companies are shedding jobs and slashing salaries.
Fitch last week cut Lebanon's credit rating for the third time in a year, warning it now expected the country to restructure or default on its debt.
Jason Tuvey, senior emerging markets economist at Capital Economics, said: "A government with a Hezbollah-backed prime minister would be even less likely to secure support from the Gulf countries...and might also potentially reduce the chances of Lebanon getting support from the IMF if the U.S. raises concerns."
A senior banker said time is running out and that politicians do not grasp the scale of the crisis. He expressed concern Hezbollah is too preoccupied with its struggle with the United States. "Right now the real battle is how to solve this real crisis - liquidity meltdown," the banker said.
Hariri did not put forward anyone for the post of prime minister and MPs with his Future Movement told Aoun it would not take part in the next government, a source close to Hariri said.
Hariri had seemed on course to be nominated prime minister himself but withdrew his candidacy on Wednesday.
That decision followed a move by the Christian Lebanese Forces, a staunchly anti-Hezbollah party with close Gulf ties, to nominate neither Hariri nor anyone else for the position.Diab served as education minister in a government led by ex-premier Najib Mikati, and is currently Vice President at the American University of Beirut.