Ackerman isn't sure:
In Brussels, NATO managed to agree on enforcing the arms embargo against Gadhafi, but it hasn’t come to a consensus on taking over the broader mission from either [Adm. Samuel Locklear] or [Gen. Carter Ham] or the U.S. overall something the Pentagon has said from the start of the war that it expects within “days.” That’s led France to seek work-arounds allowing a French-led coalition to press the attack. Reportedly, it wants a “political steering committee outside NATO” to run the war, which would have the benefit of adding the Arab League under its banner, an organization wary of working under NATO.
[T]here is still no agreement to whom command will be passed. British Prime Minister Cameron insists it must be NATO; Sarkozy insists not. The French defense spokesman now suggests all participating military forces should have the honor of serving under French national command. Turkish Defense Minister expressed mystification, saying "It does not seem quite possible for us to understand France's being so much at the forefront in this action." Italian Foreign Minister Frattini threatens Italy will not allow use of its bases unless it becomes a NATO operation.