The US, UK and France have been calling for air operations, given the reluctance of Damascus to allow relief into rebel-held areas.
This comes as Syria says it has approved the delivery of aid to 36 regions, including 11 besieged areas.
Meanwhile, air strikes in and around the northern city of Aleppo have reportedly killed 31 civilians.
They included 10 people on a bus going down a road used by rebels as a supply route, rescue workers from the Syrian Civil Defence force said.
Stephen O'Brien, the UN aid chief, told the Security Council that consent from Damascus was needed to carry out the air operations, diplomats who were in the closed door meeting said.
The formal request would be made on Sunday, they added.
The UN has 19 areas designated as "besieged" in the country, where an estimated 600,000 people live.
The UN's World Food Programme (WFP) said it had already drawn up a plan to carry out air drops but that funding was also needed.
However, a senior UN official warned that air operations were "not imminent".
Earlier, a statement by the Syrian Mission to the UN said permissions for humanitarian aid included access to Kafr Batna, Saqba, Hammura, Jisrein, Zabadin, East Harasta, Zamalka, Madaya, Foua, Kefraya and Yarmouk.
Eight other towns were approved to receive medical assistance, school supplies and milk for children, including Daraya and Douma, also under siege, it said.
The Syrian opposition has warned the government may open the door just enough to alleviate international pressure before restricting access again.
In February, the WFP carried out a 21-pallet air drop of aid to a government-held area of Deir al-Zour in eastern Syria, which ended in failure. Of the 21 pallets, 10 were unaccounted for, seven landed in no-man's land and four were damaged.
But it has since carried out 44 air drops over the city, delivering mainly rice, chickpeas and beans to meet the immediate needs of around 100,000 residents.
The WFP has identified some 592,700 people in 19 besieged areas that may need to receive aid by air.
But the operating conditions are challenging, it says. Many besieged locations are in built-up, urban areas with no suitable space for a drop zone. High-altitude drops are not possible in those areas because of the risk of harming people on the ground.
The UN food agency says airdrops are always a last resort as access by land is more efficient.
Meanwhile, aircraft from the US-led coalition dropped ammunition to rebels in the town of Marea, in Aleppo province, the UK-based monitoring group Syrian Observatory for Human Rights said.
It was not clear if weapons were also delivered.
Rebels are fighting militants from so-called Islamic State (IS), who cut off supply routes between Marea and Azaz, both under rebel control, near the Turkish border.
The area between the city of Aleppo and the Turkish border is split between IS, rebel and government-controlled zones.
The US is also supporting an offensive by the Syrian Democratic Forces (SDF), made up by Kurdish and Arab fighters, against IS-held Manbij.
The Syrian Observatory also said Islamist insurgents, including from the al-Qaeda linked al-Nusra Front, and government forces have attacked each other near Khan Touman, in southwest Aleppo.
The United Nations will ask Syria to allow the air drop of humanitarian aid to areas under siege, diplomats say.