Artificial intelligence (AI) sentience has become an important topic of discourse and inquiry in light of the remarkable progress and capabilities of large language models (LLMs). While others have considered this issue from more philosophical and metaphysical perspectives, we present an alternative set of considerations grounded in sociocultural theory and analysis. Specifically, we focus on sociocultural perspectives on interpersonal relationships, sociolinguistics, and culture to consider whether LLMs are sentient. Using examples grounded in quotidian aspects of what it means to be sentient along with examples of AI in science fiction, we describe why LLMs are not sentient and are unlikely to ever be sentient. We present this as a framework to reimagine future AI not as impending forms of sentience but rather a potentially useful tool depending on how it is used and built.