The official, who spoke on condition of anonymity, told CNN Tuesday the four NATO coalition members killed in the attack were all Americans.
The U.S.-led International Security Assistance Force confirmed the attack on Bagram but identified the victims only as "NATO coalition service members."
The Taliban issued a statement claiming responsibility for the attack.
News of the casualties came as NATO-led troops transferred security responsibility to Afghan forces.
Notable deaths of 2014 [PHOTOS]
Syrian Al Qaida group executes Lebanese soldier