The respiratory condition COVID-19 arises in a human host upon the infection with SARS-CoV-2, a coronavirus that was first acknowledged in Wuhan, China, at the end of December 2019 after its outbreak of viral pneumonia. The full-blown COVID-19 can lead, in susceptible individuals, to premature death because of the massive viral proliferation, hypoxia, misdirected host immunoresponse, microthrombosis, and drug toxicities. Alike other coronaviruses, SARS-CoV-2 has a neuroinvasive potential, which may be associated with early neurological symptoms. In the past, the nervous tissue of patients infected with other coronaviruses was shown to be heavily infiltrated. Patients with SARS-CoV-2 commonly report dysosmia, which has been related to the viral access in the olfactory bulb. However, this early symptom may reflect the nasal proliferation that should not be confused with the viral access in the central nervous system of the host, which can instead be allowed by means of other routes for spreading in most of the neuroanatomical districts. Axonal, trans-synaptic, perineural, blood, lymphatic, or Trojan routes can gain the virus multiples accesses from peripheral neuronal networks, thus ultimately invading the brain and brainstem. The death upon respiratory failure may be also associated with the local inflammation- and thrombi-derived damages to the respiratory reflexes in both the lung neuronal network and brainstem center. Beyond the infection-associated neurological symptoms, long-term neuropsychiatric consequences that could occur months after the host recovery are not to be excluded. While our article does not attempt to fully comprehend all accesses for host neuroinvasion, we aim at stimulating researchers and clinicians to fully consider the neuroinvasive potential of SARS-CoV-2, which is likely to affect the peripheral nervous system targets first, such as the enteric and pulmonary nervous networks. This acknowledgment may shed some light on the disease understanding further guiding public health preventive efforts and medical therapies to fight the pandemic that directly or indirectly affects healthy isolated individuals, quarantined subjects, sick hospitalized, and healthcare workers.