In this paper, we propose a method to estimate the proximity of an acoustic reflector, e.g., a wall, using ego-noise, i.e., the noise produced by the moving parts of a listening robot. This is achieved by estimating the times of arrival of acoustic echoes reflected from the surface. Simulated experiments show that the proposed non-intrusive approach is capable of accurately estimating the distance of a reflector up to 1 meter and outperforms a previously proposed intrusive approach under loud ego-noise conditions. The proposed method is helped by a probabilistic echo detector that estimates whether or not an acoustic reflector is within a short range of the robotic platform. This preliminary investigation paves the way towards a new kind of collision avoidance system that would purely rely on audio sensors rather than conventional proximity sensors.