In our current study, we systematically report the four phenol classes via three-layer in silico screening approaches consisting of quantum chemical methods, molecular docking and molecular dynamics simulations. We studied the interactions of main protease (Mpro) and Nsp9 proteins of SARS-CoV-2 with four classes of polyphenolic compounds, where both proteins are crucial for virus replication. The phenols are extensively reported for medicinal applications, as these are antioxidants, anti-parasitic, anti-viral, anti-diabetic and anti-inflammatory compounds. Initial molecular docking study shows that among forty phenolic compounds the L9, L17, L26 and, L32 reveal the best binding energies with Mpro protein. Their values of docking score in terms of binding energy with Mpro protein is ranging from -5.7 to -6.8 kcal.mol−1. While on the other hands, L8, L11, L22 and, L34 exhibit the best docking scores with Nsp9 protein, which are ranging from -5.8 to -6.8 kcal.mol−1. Additionally, the lead compounds (ligands) were studied by quantum chemical methods for their optimized or the lowest energy structures, electronic properties, frontier molecular orbitals (FMOs) as well as molecular electrostatic potentials (MEPs). The global chemical descriptors are also calculated to explain the global reactivity trend for the lead compounds. To mimic the aqueous like environment, we added ions according to the electrostatic potential of the macromolecule, water molecules are being added to create physiologically relevant environment for studying biological molecules. Proteins, nucleic acids, and other biomolecules are typically surrounded by water molecules in biological systems. The addition of water molecules in MD simulations may provide a more accurate representation of their natural environment. The molecular dynamics simulations are performed for the complexes of best-docked lead compounds and for both proteins (Mpro and, Nsp9) over multiple replicate trajectories of 320 ns. The flexibility and stability behavior of the lead compounds in terms of RMSD and RMSF plots are analyzed through MD simulations results. The binding free energy of the best-docked lead compounds with both proteins in terms of Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) analysis are calculated, which are found as -8.79 and -3.97 kcal.mol−1 for Mpro-L32 and Nsp9-L8 complexes, respectively. The pharmacokinetic analysis of the lead compounds are also performed to disclose their ADME (absorption, distribution, metabolism, and excretion) and toxic character using online server pkCSM. This allowed for a comprehensive understanding of how these compounds would behave in the organism, specifically focusing on their ADME properties. We believe that the current study can evoke the interest of scientific community by providing fundamental insights, which will ultimately lead in-vivo and in-vitro analysis to assess the studied phenolic therapeutic inhibitors against the SARS-CoV-2.