The European Union's Operation Sophia would be tasked with enforcing a UN arms embargo that was imposed on Libya in 2011, during the uprising against Moamer Kadhafi.
European powers are also looking at building up Libya's coast guards to ramp up operations against migrant smugglers operating off the coast of the north African country.
The two measures could "come up pretty soon" at the Security Council, said a senior diplomat, who spoke on condition that he not be named.
Operation Sophia's enforcement of the arms embargo would be aimed at shoring up the UN-backed government of Prime Minister Fayez al-Sarraj.
Many deliveries of weapons by sea have been destined for Sarraj's rival government in eastern Libya.
Sarraj won backing from the United States, European powers, Egypt and others on Monday for exemptions to the arms embargo that will allow his government to purchase weapons and confront the threat from the Islamic State group.
The draft resolution on expanding the EU naval mission would first require a decision from the European Union, said the diplomat, adding that this should take "weeks, not days."
Operation Sophia's new UN mandate would be limited however to the high seas off Libya's coast. It would authorize EU military action without the consent of the vessel's flagged state.
"If they spot that weapons are coming into Libya by sea, then they would be able to interdict the vessels carrying those weapons," he said.
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- Loosening the arms embargo -
World powers hope the new UN-backed government will be able to put an end to years of chaos in Libya since the fall of Kadhafi and confront IS jihadists who have expanded their foothold in the lawless country.
Sarraj's government has the backing of the central bank and the national oil corporation but the House of Representatives has refused to endorse the new leadership.
Libya has had two administrations since mid-2014 when the militia alliance overran Tripoli, setting up its own authority and forcing the parliament to flee to the country's remote east.
A UN panel of experts reported in March that the Tobruk-based government in the east had recently received MIG-21F jets apparently from Egypt. Cairo told the panel the information was "incorrect".
The panel is also investigating weapons deliveries from Turkey, the United Arab Emirates and Sudan to various Libya factions.
Last year, seven council members led by Spain put on hold Libya's request for UN approval of a major delivery of weaponry.
Libya had asked an exemption for deliveries of eight helicopters, six fighter jets, four fighter-bombers, 150 tanks, 150 personnel carriers mounted with machine guns, 10,000 automatic grenade launchers, 1,000 sniper rifles along with ammunition and mortar shells.
The UN experts had advised the council to reject the request, arguing that the arms shipments could fall into the wrong hands.