Hybrid beamforming is a promising technology for 5G millimetre-wave communications. However, its implementation is challenging in practical multiple-input multiple-output (MIMO) systems because non-convex optimization problems have to be solved, introducing additional latency and energy consumption. In addition, the channel-state information (CSI) must be either estimated from pilot signals or fed back through dedicated channels, introducing a large signaling overhead. In this paper, a hybrid precoder is designed based only on received signal strength indicator (RSSI) feedback from each user. A deep learning method is proposed to perform the associated optimization with reasonable complexity. Results demonstrate that the obtained sum-rates are very close to the ones obtained with full-CSI optimal but complex solutions. Finally, the proposed solution allows to greatly increase the spectral efficiency of the system when compared to existing techniques, as minimal CSI feedback is required.