Cognitive decline and hearing loss are common in older adults and often co-occur while investigated separately, affecting the neural processing of speech. This study investigated the interaction between cognitive decline, hearing loss, and contextual cues in speech processing. Participants aged 60 years and older were assessed for cognitive decline using the Montreal Cognitive Assessment and for hearing ability using a four-frequency pure tone average. They listened to in-house-designed matrix-style sentences that either provided supportive context or were random. Neurophysiological responses were analyzed through auditory evoked potentials and speech tracking at different linguistic timescales (i.e., phrase, word, syllable and phoneme rate) using phase-locking values. The results showed that cognitive decline was associated with a lower chance of correct responses in a speech recognition task. Cognitive decline significantly impacted the P2 component of auditory evoked potentials, while hearing loss influenced speech tracking at the word and phoneme rates, but not at the phrase or syllable rates. Contextual cues enhanced speech tracking at the syllable rate. These findings suggest that cognitive decline and hearing loss differentially affect the neural mechanisms underlying speech processing, with contextual cues playing a significant role in enhancing syllable rate tracking. This study emphasises the importance of considering both cognitive and auditory factors when studying speech processing in older people and highlights the need for further research to investigate the interplay between cognitive decline, hearing loss and contextual cues in speech processing.