We propose an active object recognition framework that introduces the recognition self-awareness, which is an intermediate level of reasoning to decide which views to cover during the object exploration. This is built first by learning a multi-view deep 3D object classifier; subsequently, a 3D dense saliency volume is generated by fusing together single-view visualization maps, these latter obtained by computing the gradient map of the class label on different image planes. The saliency volume indicates which object parts the classifier considers more important for deciding a class. Finally, the volume is injected in the observation model of a Partially Observable Markov Decision Process (POMDP). In practice, the robot decides which views to cover, depending on the expected ability of the classifier to discriminate an object class by observing a specific part. For example, the robot will look for the engine to discriminate between a bicycle and a motorbike, since the classifier has found that part as highly discriminative. Experiments are carried out on depth images with both simulated and real data, showing that our framework predicts the object class with higher accuracy and lower energy consumption than a set of alternatives.