Disturbed sleep and daytime sleepiness may interfere with possible direct relationships between heart failure (HF) and cognition, yet there is limited research investigating this relationship. We aimed to investigate possible mediating roles of disturbed sleep and daytime sleepiness on the relationship between HF and selected cognitive domains among individuals with and without HF. In a cross-sectional design study, we examined the data of 841 older adults with and without HF from the Aging, Demographics, and Memory Study (ADAMS). We found individuals with HF were likely to have a higher degree of disturbed sleep and daytime sleepiness. Both disturbed sleep and daytime sleepiness were significant predictors of cognition. We found that only daytime sleepiness mediated the relationship between the presence of HF and cognitive domains, such as in attention, memory, and executive function after controlling for covariates. Interventions to improve daytime sleepiness among individuals with HF may also help improving cognition.