The binding of drugs to plasma proteins, such as human serum albumin (HSA), encompasses two main functions: depot and transport, which are performed by these proteins. This binding has significant pharmacodynamic and pharmacokinetic consequences. 2-(furan-2-yl)-1H-imidazo[4,5-f][1,10]phenanthroline 1,2-diamino cyclohexane platinum (Pt(II)) or palladium (Pd(II)) complexes, have a similar structure. These new synthetic complexes have desirable anticancer activity, and the binding of these complexes with HSA was investigated. Spectroscopic and thermodynamic analyses indicate that the interactions between HSA and the complexes occur spontaneously with the static-dynamic quenching mechanism. However, the interactions are primarily driven by noncovalent forces such as hydrophobic interactions and π–π stacking, as evidenced by the positive enthalpy and entropy values associated with these complexes. In the circular dichroism (CD) results, HSA had fewer structural changes with the addition of the Pt(II) than the Pd(II) complex. Docking studies were performed at three Sudlow sites, I, II, and III, to identify the complex’s binding site on HSA. The reactive sites of HSA to Pt(II) and Pd(II) complexes mainly reside within its hydrophobic cavity in domain II (site II). Furthermore, molecular dynamics simulations showed low RMSD, Rg, and binding energy values during the 400 ns for the Pt(II) complex. The results suggest that the connection between the Pt(II) complex and HSA is reversible. The Pt(II) complex was a more desirable candidate than the Pd(II) complex. The results of the experimental methods are consistent with those of dynamic simulation and molecular docking methods, indicating that HSA is more stable in the presence of the Pt(II) complex.