We describe an interactive learning strategy that enables a humanoid robot to build a representation of its workspace: we call it a Reachable Space Map. The robot learns this map autonomously and online during the execution of goal-directed reaching movements; reaching control is based on kinematic models that are learned online as well. The map can be used to estimate the reachability of a fixated object and to plan preparatory movements (e.g. bending or rotating the waist) that improve the effectiveness of the subsequent reaching action. Three main concepts make our solution innovative with respect to previous works: the use of a gaze-centered motor representation to describe the robot workspace, the primary role of action in building and representing knowledge (i.e. interactive learning), the realization of autonomous online learning. We evaluate our strategy by learning the workspace of a simulated humanoid robot and we show how this knowledge can be exploited to plan and execute complex actions, like whole-body bimanual reaching.