To what extent do domain-general and domain-specific neural networks generalise across interactions with human and artificial agents? In this exploratory study, we analysed a publicly available fMRI dataset (n = 22; Rauchbauer, et al., 2019) to probe the similarities and dissimilarities in neural architecture while participants conversed with another person or a robot. Incorporating trial-by-trial dynamics of the interactions, listening and speaking, we used whole-brain, region-of-interest, and functional connectivity analyses to test response profiles within and across social or non-social, domain-specific and domain-general networks, i.e., the person perception, theory-of-mind, object-specific, language, multiple-demand networks. Listening to a robot compared to a human resulted in higher activation in the language network, especially in areas associated with listening comprehension, and in the person perception network. No differences in activity of the theory-of-mind network were found. Results from the functional connectivity analysis showed no difference between interactions with a human or robot in within- and between-network connectivity. Together, these results suggest that while similar regions are activated during communication regardless of the type of conversational agent, activity profiles during listening point to a dissociation at a lower-level or perceptual level, but not higher-order cognitive level.