In this paper, we introduce a novel approach to safe learning-based Model Predictive Control (MPC) for nonlinear systems. This approach, which we call the "compatible model approach", relies on computing two models of the given unknown system using data generated from the system. The first model is a set-valued over-approximation guaranteed to contain the system's dynamics. This model is used to find a set of provably safe controller actions at every state. The second model is a single-valued estimation of the system's dynamics used to find a controller that minimises a cost function. If the two models are compatible, in the sense that the estimation is included in the overapproximation, we show that we can use the set of safe controller actions to constrain the minimisation problem and guarantee the feasibility and safety of the learning-based MPC controller at all times. We present a method to build an over-approximation for nonlinear systems with bounded derivatives on a partition of the states and inputs spaces. Then, we use piecewise multi-affine functions (defined on the same partition) to calculate a system's dynamics estimation that is compatible with the previous over-approximation. Finally, we show the effectiveness of the approach by considering a path-planning problem with obstacle avoidance.