From a multidimensional perspective, empathy is a process that includes affective sharing and imagining and understanding the emotions of others. The primary brain structures involved in mediating the components of empathy are the anterior insula (AI), the anterior cingulate cortex (ACC), and specific regions of the medial prefrontal cortex (MPFC). The AI and ACC are the main nodes in the salience network (SN), which selects and coordinates the information flow from the intero- and exteroreceptors. AI might play a role as a crucial hub - a dynamic switch between 2 separate networks of cognitive processing: the central executive network (CEN), which is concerned with effective task execution, and the default mode network (DMN), which is involved with self-reflective processes. Given various classifications, a deficit in empathy may be considered a central dysfunctional trait in narcissism. A recent fMRI study suggests that deficit in empathy is due to a dysfunction in the right AI. Based on the acquired data, we propose a theoretical model of imbalanced SN functioning in narcissism in which the dysfunctional AI hub is responsible for constant DMN activation, which, in turn, centers one's attention on the self. This might hinder the ability to affectively share and understand the emotions of others. This review paper on neural mechanisms of empathy deficits in narcissism aims to inspire and direct future research in this area.