At DESY the currently available electron gun is based on a normal conductive copper cavity operated in pulsed mode. It will be replaced by a superconducting variant to enable also CW operation. The required electromagnetic field in the cavity is then excited by a dedicated input-coupler system originating from the well-known TESLA input power coupler. Additional HOM couplers are not considered in the current design phase but may be added if required. Due to the asymmetric coupling of the resonator fields to the external sources the extracted electron beam will observe a parasitic coupler kick which has to be minimized.