Taliban spokesman Zabiullah Mujahid told The Associated Press that a Taliban bomber wearing a military uniform and a suicide vest entered the base in Khost and blew himself up inside the gym.
A U.S. Congressional official told AP that CIA employees are believed to be among the dead in the Wednesday bombing.
The CIA has not yet commented on or confirmed the deaths.
The congressional official said it was not clear how many of the victims were assigned to the CIA. The official was not authorized to discuss the matter with the media, and spoke on condition of anonymity.