As simply as I can put it:
No, it is unfortunately not possible to to add an internal hard drive to your AirPort Extreme.
A hard drive will physically fit into the internal cavity of the AirPort Extreme, but the electronics necessary to make the drive work are absent on the AirPort Extreme's logic board (areas highlighted in green below).
However, you can connect an external hard drive to the AirPort Extreme's rear USB port. By going into AirPort Utility and Time Machine preferences, you can use that external USB hard drive as a wireless Time Machine backup drive.
Hope this helps!