The expected number of drone operations in the coming decades, together with the fact that most of them will take place in very-low-level airspace, will lead to a density of drone flights much greater than that of conventional manned aviation. In this context, the number of conflicts (i.e., 4D convergence of drone trajectories below the safe separation minima) will be much more frequent than in manned aviation and, therefore, conventional air traffic management methods or even the specific proposed mechanisms for drone traffic management are unlikely to be able to solve them safely. This paper considers a set of simulated drone trajectories in a high-density urban environment to analyze the applicability of machine learning regression and classification techniques to detect conflicts among such trajectory times in advance of their occurrence in order to provide new methods to manage the expected drone traffic density safely and efficiently. This would not be possible with current drone traffic management solutions. The obtained results suggest that the Random Forest, Artificial Neural Networks and Logistic Regression algorithms could detect nearly all near-collisions up to 10 s before they occur, and the first two algorithms could also detect a significant number of near-collisions more than 60 s earlier.