Relaxation behavior of structural change at the atomic cluster level in supercooled liquids during isothermal annealing processes is investigated for a model alloy system by using molecular dynamics simulations. The simulation results show that the number density of icosahedral clusters increases with the annealing time. Moreover, the number density of icosahedral clusters, the structural relaxation time, and the atomic diffusivity strongly correlate with the packing density of the supercooled liquids for many kinds of systems of alloying components with a variety of atomic size ratios and heats of mixing. This suggests that the packing density would be a good probe to estimate the stability of supercooled liquid phases and the glass-forming ability of the system.