To interact with its environment, a robot working in 3D space needs to organise its visual input in terms of objects or their perceptual precursors, proto-objects. Among other visual cues, depth is a submodality used to direct attention to visual features and objects. Current depth-based proto-object attention models have been implemented for standard RGB-D cameras that produce synchronous frames. In contrast, event cameras are neuromorphic sensors that loosely mimic the function of the human retina by asynchronously encoding per-pixel brightness changes at very high temporal resolution, thereby providing advantages like high dynamic range, efficiency (thanks to their high degree of signal compression), and low latency. We propose a bio-inspired bottom-up attention model that exploits event-driven sensing to generate depth-based saliency maps that allow a robot to interact with complex visual input. We use event-cameras mounted in the eyes of the iCub humanoid robot to directly extract edge, disparity and motion information. Real-world experiments demonstrate that our system robustly selects salient objects near the robot in the presence of clutter and dynamic scene changes, for the benefit of downstream applications like object segmentation, tracking and robot interaction with external objects.