Sleep's role in memory consolidation is widely acknowledged, but its role in weakening memories is still debated. Memory weakening is evolutionary beneficial and makes an integral contribution to cognition. We sought evidence on whether sleep-based memory reactivation can facilitate memory suppression. Participants learned pairs of associable words (e.g., DIET-CREAM) and were then exposed to hint words (e.g., DIET) and instructed to either recall ("think") or suppress ("no-think") the corresponding target words (e.g., CREAM). As expected, suppression impaired retention when tested immediately after a 90-min nap. To test if reactivation could selectively enhance memory suppression during sleep, we unobtrusively presented one of two sounds conveying suppression instructions during sleep, followed by hint words. Results showed that targeted memory reactivation did not enhance suppression-induced forgetting. Although not predicted, post-hoc analyses revealed that sleep cues strengthened memory, but only for suppressed pairs that were weakly encoded before sleep. The results leave open the question of whether memory suppression can be augmented during sleep, but suggest strategies for future studies manipulating memory suppression during sleep. Additionally, our findings support the notion that sleep reactivation is particularly beneficial for weakly encoded information, which may be prioritized for consolidation.