Taliban spokesman Zabiullah Mujahid said, "A Taliban bomber wearing a military uniform and a suicide vest entered a base in Khost and blew himself up inside the gym."
A US Congressional official said that CIA employees are believed to be among the dead.
The CIA has not yet commented on or confirmed the deaths.
The Khost bombing was one of the highest American civilian death tolls in a single incident during the Afghanistan and Iraq wars.
Khost, in eastern Afghanistan, is one of the centres of the Taliban insurgency. Most foreigners working there are soldiers or contractors working in reconstruction and intelligence operations.