Lithium-ion batteries are complex systems that require suitable management strategies to work properly, achieve fast charging, mitigate ageing mechanisms and guarantee safety. Among the different model-based charging strategies, the use of predictive control has shown promising results, due to its ability to deal with nonlinear systems subject to safety constraints. However, although many implementations have been proposed in the literature, little attention has been paid to their practical feasibility, which is limited by the high computational cost required online. In this paper, we exploit, for the first time in the batteries field, an approximation of predictive control obtained through the use of a deep neural network. The proposed solution is suitable for real-time battery charging, due to the fact that most of the computational burden is addressed offline. The results highlight the effectiveness of the presented methodology in approximating a standard model predictive control solution.