We introduce a novel computational framework inspired by the physics of nanowire memristive networks, which we embed into the context of Recurrent Neural Networks (RNNs) for time-series processing. Our proposed Nanowire Neural Network architecture leverages both the principles of Reservoir Computing (RC) and fully trainable RNNs, providing a versatile platform for sequence learning. We demonstrate the effectiveness of the proposed approach across diverse regression and classification tasks, showcasing performance that is competitive with traditional RC and fully trainable RNNs. Our results highlight the scalability and adaptability of nanowire-based architectures, offering a promising path toward efficient neuromorphic computing for complex sequence-based applications.