The administration asked senior military leaders to develop the options. The move reflects the long-running debate over how many U.S. troops are needed to advise Afghan forces and conduct counterterrorism missions.
The official was not authorized to talk on the record by name and spoke on condition of anonymity.
Some officials argue the larger number is needed to conduct the missions and provide security for the troops. Others say Afghan forces have improved so fewer U.S. forces are needed.
Combat operations will end Dec. 31. Earlier plans called for leaving 8,000 to 12,000 troops there as long as Afghan leaders sign a security agreement.