This paper proposes a novel wireless relay selection scheme involving multiple mobile Unmanned Aerial Vehicles (UAVs) to support communicating ground users. The goal is to optimize the transmit power levels and trajectories of the relaying UAVs in order to maximize the data rate transmission of the ground users which are suffering from the absence of direct link. Assuming that each UAV is initially characterized by a predefined trajectory for a primary task, we propose to modify it whenever it is needed and the energy and trajectory boundaries constraints allow. We propose to solve this problem using an iterative two steps solution; first, a Mixed Integer Linear Programming (MILP) problem is formulated to optimally determine the users- UAVs associations and the UAVs' corresponding transmit power levels. In the second step, an efficient algorithm based on a recursive shrink-and-realign process is proposed to optimize the UAV trajectories. The performance of the proposed method shows advantages in terms of average throughput compared to the predefined trajectories solution.