In this work we address the speaker verification task in domestic environments, monitored by multiple distributed microphones. In particular, we focus on the problem of mismatch in the propagation channel between the enrolment stage, which occurs at a fixed position, and the test phase which could happen in any location of a multi-room apartment. Building upon the Total Variability framework and cosine distance scoring, we present two multi-channel solutions: one based on multi-condition training and the other based on several channel-dependent systems. An experimental analysis on a multi-channel multi-room reverberant data-set shows that the proposed solutions are robust against changes in the speaker position and orientation and improve the performance of the single-channel matched baselines.