The Department of Homeland Security did not immediately agree to do so because it wanted to make sure that Mrs Pinochet was not acting under coercion, the official said on Friday.
The official said reviews in such cases are routine. If the government allows her to drop her request, Pinochet is likely to be ordered out of the country, said the official who was not authorised to discuss the matter publicly and spoke only on condition of anonymity.
Pinochet, 60, was detained on Wednesday when she attempted to enter the United States at Dulles International Airport outside Washington, arriving on a flight from Argentina.
Suzanne Trevino, a spokeswoman for US Customs and Border Protection at the Department of Homeland Security, said asylum seekers who are not admitted to the United States are put on a flight to the country from which they had departed.