In this paper, we propose a novel energy harvesting (EH)-aware sensor selection policy. Our goal is to minimize the distortion in the reconstruction of the underlying source subject to the causality constraints imposed by the EH process at the sensor nodes. Besides, we determine the optimal power allocation for a given sensor selection (which admits a two-dimensional directional waterfilling interpretation) as the solution of an offline convex optimization problem. To that aim, we propose an iterative procedure. Performance is assessed by means of simulations and a lower bound that we also establish.