Adaptive beamformers have been proposed as noise reduction schemes for conventional hearing aids and cochlear implants. A method to predict the amount of noise reduction that can be achieved by a two-microphone adaptive beamformer is presented. The prediction is based on a model of the acoustic environment in which the presence of one acoustic target-signal source and one acoustic noise source in a reverberant enclosure is assumed. The acoustic field is sampled using two omnidirectional microphones mounted close to the ears of a user. The model takes eleven different parameters into account, including reverberation time and size of the room, directionality of the acoustic sources, and design parameters of the beamformer itself, including length of the adaptive filter and delay in the target signal path. An approximation to predict the achievable signal-to-noise improvement based on the model is presented. Potential applications as well as limitations of the proposed prediction method are discussed and a FORTRAN subroutine to predict the achievable signal-to-noise improvement is provided. Experimental verification of the predictions is provided in a companion paper [J. Acoust. Soc. Am. 109, 1134 (2001)].