Dynamic obstacle avoidance is an essential function for Unmanned Aerial Vehicles (UAVs) to ensure the safe and reliable operations of drones in real-world environments. It allows drones to navigate and react to environmental changes in real time, preventing collisions and maintaining their flight paths. Dynamic obstacle avoidance also improves the success rate of the drone's mission by reducing the need for manual control. In this study, we propose a model predictive control (MPC) concept to generate high-level control commands for drones to avoid dynamic obstacles by integrating Gaussian process regression to forecast the motion of the moving obstacle based on noisy observations. Additionally, we also investigated the applicability of the Kalman filter as an alternative approach in this context. Our tests demonstrate promising results for multi-rotor drones in physics-based simulations.