Anticipating opposition, Britain's foreign minister has insisted that there must be "a clear legal basis" for the zone and set other conditions.
"You should expect something on Libya this week," one UN diplomat told AFP on condition of anonymity, confirming that France and Britain are drawing up a resolution. "There is a feeling of urgency now."
"There are elements of a text ready which can be distributed to the council. It could well be this week," said a British diplomat.
Britain and France have made the most aggressive calls among Western powers for a no-fly zone to hamper Kadhafi's offensive. The United States has said it is studying the possibility while warning of the major military operation it would entail.
The UN Security Council unanimously passed sanctions against the Kadhafi regime and ordered a crimes against humanity investigation on February 26. Any new move toward military action is likely to face tough resistance from China, Russia and other members of the 15 however.
Britain's Foreign Secretary William Hague said the Libyan rebels had "explicitly" asked for action to prevent Kadhafi's air attacks but that "many conditions should be attached" to any no-fly zone.
"At the UN Security Council we are working closely with partners on a contingency basis on elements of a resolution on a no-fly zone, making clear the need for regional support, a clear trigger for such a resolution and an appropriate legal basis," Hague told the British parliament.
"There should be a demonstrable need that the whole world can see, there must be a clear legal basis for such a no-fly zone and there must be clear support from the region, from the Middle East region, from the North African region as well as from the people of Libya themselves," he said.
"I think those are the necessary conditions for such a no-fly zone to be created."
Arab League secretary general Amr Mussa supported a no-fly zone when he spoke to French Foreign Minister Alain Juppe in Cairo on Sunday, French foreign ministry spokesman Bernard Valero said in Paris.
The six-nation Gulf Cooperation Council also released a statement on Monday backing a no-fly zone.
Strong support from Arab and African nations helped sway Russia, China and others behind the assets freeze and travel ban against Kadhafi and 15 other members of his family and regime.
Russia and China, which traditionally oppose military sanctions, may resist stronger measures so soon after the last vote, diplomats and experts said.
Russia, China, Britain, France and the United States are permanent members of the Security Council with the power to veto any resolution.
Russia's Foreign Minister Sergei Lavrov last week called the no-fly zones "superfluous" and said international powers should concentrate on the existing sanctions.
"We do not consider foreign and especially military intervention a means to resolve the crisis in Libya," Russian news agencies quoted Lavrov as saying Monday. "The Libyans must resolve their problems themselves."
China's foreign ministry also indicated last week that it was cool to military action.
India, also a member of the Security Council, has opposed no-fly zones, though diplomats said it could be swayed if the Libya fighting worsens.
------------------------------------------------------------------------------------