We consider a wireless source localization network in which eavesdropper nodes aim to estimate the position of a target node. We formulate the problem of selecting a set of N E positions out of N possible positions for placing eavesdropper nodes in order to estimate the target node position as accurately as possible. The Cramér-Rao lower bound related to the estimation of the target node position by eavesdropper nodes is derived, and its monotonicity and convexity properties are investigated. Via relaxation of the integer constraints, the eavesdropper selection problem is approximated by a convex optimization problem, which is used to propose two algorithms for eavesdropper selection. Moreover, in the presence of parameter uncertainty, a robust version of the eavesdropper selection problem is investigated. Simulation results are presented to examine performance of the proposed algorithms.