Michel Sleiman, Lebanon's president, held consultations with parliamentarians on Friday to discuss candidates to be the next prime minister. He is expected to officially designate Hariri on Saturday.
"We have chosen as our candidate for the premiership the head of the Future Movement, Saad Hariri," Samir el-Jisr, a party official and MP, said after meeting Sleiman.
The premiership must be held by a Sunni Muslim under Lebanon's sectarian power-sharing constitution, which divides the main political positions between the countries religious groups.
While the 71 MPs from Hariri's majority coalition could effectively appoint him as prime minister, he has reached out to his powerful rivals in the March 8 bloc in an attempt to guarantee a smooth transition into his administration.
The Future Movement leader backed Nabih Berri, leader of the Amal movement, for re-election as parliamentary speaker on Thursday in a symbolic sign of reconciliation.
Amal is part of the opposition coalition which includes Hezbollah. The two Shia Muslim groups have 25 MPs between them.
Lamis Adoni, Al Jazeera's Middle East analyst, said: "The meeting [between Hariri and Nasrallah] should also be viewed in the context of mostly unpublicised deliberations between Syria and Saudi Arabia over the formation of a new Lebanese government.
"It has become clear that a Syrian-Saudi understanding is crucial for the formation of a consensus government headed by Saad al-Hariri.
"It is also an indication that Hezbollah remains a major player, even though the opposition coalition lost the elections, the party itself maintained strong support in its areas."
Hariri was raised in Saudi Arabia and is seen by some in Lebanon as a symbol of Riyadh's influence in the region, which is rivalled by Damascus.
Nasrallah has previously called for the formation of a national unity government with veto power for the minority alliance after the parliamentary election, but Hariri has rejected such a veto.
It was not clear whether this issue was raised during the meeting between the two men.
Hariri entered politics in 2005 after the assassination of his father, a former prime minister.
He quickly became the strongest Sunni leader in a country and called for the contentious issue of disarming Hezbollah to be shelved in hopes of offering new incentive for the group's support.
Instead Hariri has focused on the need to improve the economy, stating his support for long-stalled economic measures including privatisation, which economists say are vital to reducing Lebanon's massive public debt burden.
He has twice passed on the chance of becoming prime minister, preferring to giving the post to his father's senior aide, Fouad Siniora, to avoid some of the political tension and direct challenge that Hezbollah posed at the time.