This paper presents a nonlinear model predictive control (NMPC) approach for trajectory tracking of a multi-UAV system with a high risk of collision. The proposed solution focuses on minimizing unnecessary complex maneuvers while ensuring collision avoidance without compromising the final position accuracy. Allocating different levels of passing priority to the agents enables fewer alternations of the initially planned path as only the agents with lower passing priority handle collision avoidance when the risk arises. The agent with a higher passing priority tracks its reference trajectory along the planned path, without considering collision avoidance. This strategy aims to perform fewer alternations and aggressive maneuvers resulting in increased safety of the multi-UAV mission.All the agents solve an unconstrained optimal control problem in a distributed manner, as collision avoidance is also defined as a cost function term that penalizes the proximity between the agents. Finally, the performance of the proposed approach is studied in simulation in the case of a two-quadcopter mission, highlighting its efficiency and robustness against external disturbances and model uncertainties.