Spike sorting is a crucial step in the analysis of multichannel neural signals that enables the identification of individual neurons’ activity. However, the limited availability of low-power neuromorphic spike sorting methods is due to the difficulty of processing high-density multichannel extracellular neural signals. In this study, we propose to use the locally competitive algorithm (LCA) that has been previously implemented on neuromorphic hardware as a novel feature extraction method for spike sorting. Based on a bio-inspired neural network, LCA can learn a signal-dependent dictionary of spatiotemporal features and give highly sparse representations. The proposed approach results in better sorting accuracy at low signal-to-noise ratios compared to k-SVD, a well-known sparse coding model, and the principal component analysis (PCA), a classical approach in spike sorting. This network-based solution paves the way for neuromorphic processing of multichannel neural signals in future brain implants.