In multiple-antenna communication systems, it is crucial for the base station to acquire accurate downlink Channel State Information (CSI) to optimize signal transmission through beamforming. However, with the absence of the channel reciprocity, the mobile station must follow the process of channel estimation with feeding the CSI back to the base station. This can introduce a substantial overhead that increases with the number of antennas and the bandwidth. therefore the CSI must be first compressed and quantized before reporting. In this paper we introduce a novel approach that based on combining Dynamic Mode Decomposition (DMD) with Residual Vector Quantization (RVQ). RVQ adapts the quantization accuracy based on the DMD output, namely the modes. This strategy allows the system to prioritize important feedback data and reduce the overhead bits needed for less critical data. Simulation results show that our approach can reduce the CSI feedback overhead while maintaining the target channel reconstruction accuracy.