Artificial intelligence-based decision-support systems (AI DSS), powered by complex algorithms, often lack transparency. To tackle this challenge, organizations deploy explainable artificial intelligence (XAI). However, studies reveal that XAI use does not necessarily result in enhanced human-XAI performance. Recently, a call has been made for more AI studies from the user perspective to better understand this phenomenon. Approaches to such studies need advancement, too. Indeed, most existing studies on cognitive mechanisms behind XAI-supported decision-making rely on integration of behavioral data and think-aloud protocols, post-hoc surveys, or interviews. Neurocognitive mechanisms behind XAI-supported decision-making remain a black box. The goal of the current paper is to provide a basis for neurophysiological studies on XAI-supported decision-making in organizational context. For this, we conduct an integrative literature review at the intersection of three domains: XAI from the user perspective; neurophysiological lens on XAI; XAI within the three-stage dual-process model of cognition.