Aphasia is a communication disorder that affects processing of language at different levels (e.g., acoustic, phonological, semantic). Neural tracking of continuous speech, such as a story, allows to analyze brain responses to acoustic and linguistic properties. Even though neural tracking of speech measured via EEG may be an interesting tool to study aphasia in an ecologically valid way, this method has not yet been investigated in individuals with stroke-induced aphasia. Here, we explored processing of acoustic and linguistic speech representations in individuals with aphasia in the chronic phase after stroke and age-matched healthy controls. We found decreased neural tracking of acoustic and segmentation-related speech representations in individuals with aphasia. In addition, linguistic speech representations at the word-level displayed decreased amplitudes in individuals with aphasia around 200 ms over left-sided frontal electrodes. These results show that there is potential for neural tracking to capture language processing impairments in individuals with aphasia. However, more research is needed to validate these results. Nonetheless, this exploratory study shows that neural tracking of naturalistic, continuous speech presents a powerful tool to study aphasia.