There are two schools of thought:
1, The US and its allies have wanted to oust Gaddafi all along and have initiated the turmoil in Libya, or, at the very least, is pleased and hopes to capitalize on it.
2, The US is terrified by the prospect of Gaddafi's fall and is inveigling to control the aftermath.
I yield the floor to Hillary Clinton:
"I am very pleased to welcome Minister Qadhafi [ son of Moammar ] here to the State Department. We deeply value the relationship between the United States and Libya. We have many opportunities to deepen and broaden our cooperation. And I’m very much looking forward to building on this relationship. So, Mr. Minister, welcome so much here." April, 2009
http://www.state.gov/secretary/rm/2009a/04/121993.htm