An addition to the target tracking application is the presence of a tracker that aims to intercept the target. The WSN provides the position of the target to the tracker, so that it can move towards the target. The objective is to reach the target in the shortest possible time, using the fewest number of nodes to save energy. In this paper, we propose and evaluate a Tracking Algorithm for Target Interception in face-structured sensor networks (TATI). TATI reduces the number of active nodes, activating only the faces that are feasible to be achieved by the target until the next sampling. Furthermore, the algorithm uses the nominal communication range of the nodes to shorten the route of the tracker. Simulation results show that TATI can save up to 15% in energy consumption, and it can keep the tracker around 10 meters closer to the target compared to the baseline.