Neurodegenerative diseases causing dementia are known to affect a person's speech and language. Part of the expert assessment in memory clinics therefore routinely focuses on detecting such features. The current outpatient procedures examining patients' verbal and interactional abilities mainly focus on verbal recall, word fluency, and comprehension. By capturing neurodegeneration-associated characteristics in a person's voice, the incorporation of novel methods based on the automatic analysis of speech signals may give us more information about a person's ability to interact which could contribute to the diagnostic process. In this proof-of-principle study, we demonstrate that purely acoustic features, extracted from recordings of patients' answers to a neurologist's questions in a specialist memory clinic can support the initial distinction between patients presenting with cognitive concerns attributable to progressive neurodegenerative disorders (ND) or Functional Memory Disorder (FMD, i.e., subjective memory concerns unassociated with objective cognitive deficits or a risk of progression). The study involved 15 FMD and 15 ND patients where a total of 51 acoustic features were extracted from the recordings. Feature selection was used to identify the most discriminating features which were then used to train five different machine learning classifiers to differentiate between the FMD/ND classes, achieving a mean classification accuracy of 96.2%. The discriminative power of purely acoustic approaches could be integrated into diagnostic pathways for patients presenting with memory concerns and are computationally less demanding than methods focusing on linguistic elements of speech and language that require automatic speech recognition and understanding.