The association of COVID-19 with neurological complications is a well-known fact, and researchers are endeavoring to investigate the mechanistic perspectives behind it. SARS-CoV-2 can bind to Toll-like receptor 4 (TLR-4) that would eventually lead to α-synuclein aggregation in neurons and stimulation of neurodegeneration pathways. Olive leaves have been reported as a promising phytotherapy or co-therapy against COVID-19, and oleuropein is one of the major active components of olive leaves. In the current study, oleuropein was investigated against SARS-CoV-2 target (main protease 3CLpro), TLR-4 and Prolyl Oligopeptidases (POP), to explore oleuropein potency against the neurological complications associated with COVID-19. Docking experiments, docking validation, interaction analysis, and molecular dynamic simulation analysis were performed to provide insight into the binding pattern of oleuropein with the three target proteins. Interaction analysis revealed strong bonding between oleuropein and the active site amino acid residues of the target proteins. Results were further compared with positive control lopinavir (3CLpro), resatorvid (TLR-4), and berberine (POP). Moreover, molecular dynamic simulation was performed using YASARA structure tool, and AMBER14 force field was applied to examine an 100 ns trajectory run. For each target protein-oleuropein complex, RMSD, RoG, and total potential energy were estimated, and 400 snapshots were obtained after each 250 ps. Docking analyses showed binding energy as −7.8, −8.3, and −8.5 kcal/mol for oleuropein-3CLpro, oleuropein-TLR4, and oleuropein-POP interactions, respectively. Importantly, target protein-oleuropein complexes were stable during the 100 ns simulation run. However, an experimental in vitro study of the binding of oleuropein to the purified targets would be necessary to confirm the present study outcomes.