This paper addresses the problem of adaptive codebook (CB) selection for downlink (DL) precoder quantization in channel state information (CSI) reporting. The accuracy of precoder quantization depends on propagation conditions, requiring independent parameter adaptation for each user equipment (UE). To enable optimal CB selection, this paper proposes UE-assisted CB selection at the base station (BS) using reported by the UE statistical channel properties across time, frequency, and spatial domains. The reported assistance information serves as input to a neural network (NN), which predicts the quantization accuracy of various CB types for each served user. The predicted accuracy is then used to select the optimal CB while considering the associated CSI reporting overhead and precoding performance. System-level simulations demonstrate that the proposed approach reduces total CSI overhead while maintaining the target system throughput performance.