An apparatus and a method for background noise estimation use a first and a second hearing device for binaural supply of a hearing impaired person. In each case the hearing devices have a first and a second omnidirectional microphone and the two microphones of each hearing device are connected to each other electrically in order to form a first and/or a second monaural directional characteristic. The first and/or second microphone of the first hearing device is connected together wirelessly with the first and/or second microphone of the second hearing device to form a binaural directional characteristic. To estimate the background noise, the level of an output signal from the first and/or the second directional microphone having a monaural directional characteristic is combined with the level of an output signal from the directional microphone having a binaural directional characteristic. Background noise estimation is thereby enhanced in the case of binaural supply.