The woman had been working for several humanitarian aid groups when she was kidnapped.
The U.S. government and the woman's family requested Tuesday that she not be named for fears of her safety.
The administration officials spoke on condition of anonymity because they were not authorized to discuss the issue publicly.
The woman is one of at least three known hostages of Islamic State militants in Syria. Another, James Foley, was beheaded by the militant group more than a week ago. Other American hostages were being held by other groups. These include Peter Curtis, who was released by al-Nusra Front earlier this week .