But, during deliberations for the past two days between parliamentarians and Suleiman, opposition parties and their ally, Christian leader Michel Aoun, withheld support from Hariri because, they said, Hariri 'did not commit to form a cabinet based on the 15-10-5 formula'.
According to the Lebanese constitution, Hariri has to name a cabinet which includes all the rival Lebanese factions and have a balanced representation in accordance with the country's religious system.
Since Hariri holds a parliamentary majority, his party has the upper hand in naming a premier, usually a Sunni Muslim according to the constitution.
On Monday Hariri said: 'when I get appointed I will start negotiating, and [then] I would assess the level of cooperation by political parties.'
Hariri's allies said that it was up to the new premier-designate to decide upon the continued validity of the 15-10-5 formula, stressing the need to resume deliberations on the cabinet issue from scratch.
'I have kept my hand extended but [the opposition] has always rejected our open approach,' he said.
Hariri is the son of late premier Rafik Hariri, who was killed in a car bomb blast in 2005 along with 20 others.