Modern approaches to speaker recognition (verification) operate in a space of "supervectors" created via concatenation of the mean vectors of a Gaussian mixture model (GMM) adapted from a universal background model (UBM). In this space, a number of approaches to model inter-class separability and nuisance attribute variability have been proposed. We develop a method for modeling the variability associated with each class (speaker) by using partial-least-squares - a latent variable modeling technique, which isolates the most informative subspace for each speaker. The method is tested on NIST SRE 2008 data and provides promising results. The method is shown to be noise-robust and to be able to efficiently learn the subspace corresponding to a speaker on training data consisting of multiple utterances.