The performance of speaker verification (SV) models may drop dramatically in noisy environments. A speech enhancement (SE) module can be used as a front-end strategy. However, existing SE methods may fail to bring performance improvements to downstream SV systems due to artifacts in the predicted signals of SE models. To compensate for artifacts, we propose a generic denoising framework named LC4SV, which can serve as a pre-processor for various unknown downstream SV models. In LC4SV, we employ a learning-based interpolation agent to automatically generate the appropriate coefficients between the enhanced signal and its noisy input to improve SV performance in noisy environments. Our experimental results demonstrate that LC4SV consistently improves the performance of various unseen SV systems. To the best of our knowledge, this work is the first attempt to develop a learning-based interpolation scheme aiming at improving SV performance in noisy environments.