The request sought permission to shoot three hours of film footage (between Tuesday and Wednesday), without the participation of people or narrative, as part of its coverage of the basketball game between the Athens club Panathinaikos and Real Madrid.
Last week KAS reversed a decision to bar filming by the BBC at the ancient site of Sounion, south of Athens.
It initially refused to grant permission, claiming the long hours requested at the site and the number of people involved would be unacceptable.
The council’s initial decision attracted strong criticism as Greece attempts to drum up much-needed investment by offering filmmakers a cost-effective destination to shoot.
KAS is said to receive more than 100 requests per year to film on the Acropolis.