Siniora, who was selected prime minister by an anti-Syrian coalition, disclosed none of the names on his list, saying pro- Syrian Lahoud promised to give his response on Wednesday.
Lahoud, whose son-in-law and outgoing Defence Minister Elias Murr was wounded in Tuesday's assassination attempt that targeted his convoy, has the final say on the cabinet lineup.
If approved by Lahoud, the new cabinet is expected to be Lebanon's first government free of Syrian dominance in three decades, following the US and UN pressured Syrian troop withdrawal from the country.
"The meeting with the president was very good, during which we reviewed many issues related to the formation of the new cabinet," Sianiora told reporters after meeting Lahoud.
Tuesday's attack deepened fears of increasing violence in the fractious nation and was the latest in a string of bombings that have killed or wounded politicians and other prominent figures in Lebanon.
While Lebanon's 128-seat parliament is dominated by the anti-Syrian coalition headed by figures such as Sianiora and Saad al-Hariri, a son of the slain ex-premier Rafiq al-Hariri, it does not have a free hand in forming the cabinet, which Lahoud must approve.
The president has signalled he would veto a cabinet list deemed favouring the anti-Syrian coalition. Many Lebanese have slammed the wrangling over the government's formation, saying it has added to the country's instability.
"These...events require a quick Cabinet formation that gains the support of all political parties"
Lebanon prime minister-designate
Siniora, a former finance minister, has underlined the urgency to announce the cabinet and deal with the security deterioration.
"These political, security and social events require a quick cabinet formation that gains the support of all political parties," said Sianiora, who was a trusted aide to the late al-Hariri.