Linear discriminant analysis (LDA) is an effective and widely used discriminative technique for speaker verification. However, it only utilizes the information on global structure to perform classification. Some variants of LDA, such as local pairwise LDA (LPLDA), are proposed to preserve more information on the local structure in the linear projection matrix. However, considering that the local structure may vary a lot in different regions, summing up related components to construct a single projection matrix may not be sufficient. In this paper, we present a speaker-aware strategy focusing on preserving distinct information on local structure in a set of linear discriminant projection matrices, and allocating them to different local regions for dimension reduction and classification. Experiments on NIST SRE2010 and NIST SRE2016 show that the speaker-aware strategy can boost the performance of both LDA and LPLDA backends in i-vector systems and x-vector systems.