Since the Cisco ASA is a security device, It does not support CDP/LLDP which collects information on neighboring NW devices.
Information on the Cisco Support Community
Several questions on ASA's CDP/LLDP compliance status are being made. The question is about ASA 5505, but it is the same specification in ASA series in general.
Note on using PoE port of ASA5505
As described in this article, when connecting a wireless AP to the PoE port of the ASA5505, if you establish a CDP neighbor with another Cisco device (such as a Catalyst switch) beyond the ASA, PoE can not supply power correctly there are cases.