Dementia affects a large proportion of the world's population. Approaches that allow for early disease detection and non-invasive monitoring of disease progression are desperately needed. Current approaches are centred on costly imaging technologies such as positron emission tomography and magnetic resonance imaging. We propose an alternative approach to assess neurodegeneration based on diffuse correlation spectroscopy (DCS), a remote and optical sensing technique. We employ this approach to assess neurodegeneration in mouse brains from healthy animals and those with prion disease. We find a statistically significant difference in the optical speckle decorrelation times between prion-diseased and healthy animals. We directly calibrated our DCS technique using hydrogel samples of varying Young's modulus, indicating that we can optically measure changes in the brain tissue stiffness in the order of 60 Pa (corresponding to a 1 s change in speckle decorrelation time). DCS holds promise for contact-free assessment of tissue stiffness alteration due to neurodegeneration, with a similar sensitivity to contact-based (e.g. nanoindentation) approaches.