The recently declared global pandemic of a new human coronavirus called SARS-CoV-2, which causes respiratory tract disease COVID-19, has reached worldwide resonance and global efforts are being made to look for possible cures. Sophisticated molecular docking software, as well as available protein sequence and structure information, offer the ability to test the inhibition of two important targets of SARS-CoV-2, furin (FUR) enzyme, and spike glycoprotein, or spike protein (SP), that are key to host cell adhesion and hijacking. The potential inhibitory effect and mechanism of action of acid–base forms of different antiviral drugs, dominant at physiological pH, chloroquine (CQ), hydroxychloroquine (HCQ), and cinanserin (CIN), which have been shown to be effective in the treatment of SARS-CoV-2 virus, is reported with the special emphasis on their relative abundances. On the other hand, the potential inhibitory effect of the dominant acid–base forms of quercetin (Q) and its oxidative metabolite 2-(3,4-dihydroxybenzoyl)-2,4,6-trihydroxy-3(2H) benzofuranone (BZF), which are constituents of traditional food products believed to exhibit antiviral effects, was also examined. The undertaken study includes the determination of the major energy contributions to the binding energy as well as in-depth analysis of amino acid residues at the active pocket and possible interactions. The approach that we propose here may be an additional strategy for combating the deadly virus by preventing the first step of the virus replication cycle. Preliminary research has shown that the investigated compounds exert an inhibitory effect against the SARS-CoV-2 furin enzyme and spiked glycoprotein through different acid–base forms. These investigations may be helpful in creating potential therapeutic agents in the fight against the SARS-CoV-2 virus. On the other hand, the results we predicted in this computational study may be the basis for new experimental in vitro and in vivo studies.