We report two complexes [Cu(LI)2] (1) and [Cu(LII)2] (2) (HLI = N-cyclohexyl-3-methoxysalicylideneimine, HLII = N-cyclohexyl-3-ethoxysalicylideneimine). The ligands in both complexes are trans-1,5-N,O-coordinated, yielding a square planar CuN2O2 coordination core. The molecule of 1 is planar with two cyclohexyl groups oriented to the opposite sites of the planar part of a molecule, while the molecule of 2 is significantly bent with two cyclohexyl groups oriented to the same convex site of a molecule. It was established that both complexes in MeOH absorb in the UV region due to intraligand transitions and LMCT. Furthermore, the UV-vis spectra of both complexes revealed two low intense shoulders in the visible region at about 460 and 520 nm, which were attributed to d–d transitions. Both complexes were predicted to belong to a fourth class of toxicity with the negative BBB property and positive gastrointestinal absorption property. According to the molecular docking analysis results, both complexes are active against all the applied SARS-CoV-2 proteins with the best binding affinity with Nsp 14 (N7-MTase), PLpro and Mpro. The obtained docking scores of complexes are either comparable to or even higher than those of the initial ligands. Complex 1 was found to be more efficient upon interaction with the applied proteins in comparison to complex 2. Ligand efficiency scores for the initial ligands, 1 and 2 were also revealed.