The current pandemic of coronavirus disease 2019 (COVID-19) has gained increased attention in the neuroscience community, especially taking into account the neuroinvasive potential of its causative agent, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and the impact of its infection on the structure and function of the brain. Apart from the neurotropic properties of SARS-CoV-2, it is likewise important the observation that virus infection may perturb specific cellular processes that are believed to play an important role in the pathogenesis of diverse neurological disorders, particularly in Parkinson's disease (PD). In this scenario, viral infection-induced colon inflammation, gut microbial imbalance, and α-synuclein upregulation are of particular interest with regard to the interplay between the gastrointestinal tract and the central nervous system (microbiome-gut-brain axis). In this Perspective, we present a critical view on the different hypotheses that are recently being raised by neuroscientists about the relationship between SARS-CoV-2 infection and long-lasting neurodegenerative disorders, opening the question of whether COVID-19 might represent a risk factor for the development of PD.