Recently, feature extraction with learnable filters was extensively investigated with speaker verification systems, with filters learned both in time- and frequency-domains. Most of the learned schemes however end up with filters close to their initialization (e.g. Mel filterbank) or filters strongly limited by their constraints. In this paper, we propose a novel learnable sparse filterbank, named LearnSF, by exclusively optimizing the sparsity of the filterbank, that does not explicitly constrain the filters to follow pre-defined distribution. After standard pre-processing (STFT and square of the magnitude spectrum), the learnable sparse filterbank is employed, with its normalized outputs fed into a neural network predicting the speaker identity. We evaluated the performance of the proposed approach on both VoxCeleb and CNCeleb datasets. The experimental results demonstrate the effectiveness of the proposed LearnSF compared to both widely-used acoustic features and existing parameterized learnable front-ends.