Local sleep refers to sleep-like slow waves occurring during wakefulness. While its exact function remains unclear, local sleep has been hypothesized to support memory consolidation. In this study, we investigated whether local sleep predicts memory consolidation in a reward-based learning paradigm and whether local sleep relates to mind wandering, a cognitive state previously linked to both local sleep and memory consolidation. Thirty-one participants completed a Swahili-English word learning task with manipulated reward contingencies, followed by recognition tests and a sustained attention to response task during which EEG and eye-tracking data were recorded. To detect local sleep, we implemented a detection algorithm in Python based on the approach by Andrillon et al. (2021). Mind wandering was measured with a task-evoked pupillary response, a physiological marker of attentional engagement. Contrary to our hypothesis, local sleep did not predict memory consolidation for high reward prediction error trials after correcting for multiple comparisons. Furthermore, local sleep showed an unexpected positive association with task-evoked pupillary response, contradicting predictions based on the mind-wandering literature. We partially replicated previous findings by Andrillon et al. (2021) linking local sleep to task performance, with local sleep in the frontal areas associated with faster reaction times and increased false alarms. Additionally, exploratory analyses revealed that local sleep exhibited substantial spatial overlap across channels (M = 53.6%), raising questions about the spatial specificity of local sleep detection. These findings question the role of local sleep in memory consolidation and highlight methodological considerations for future research examining the function of local sleep.