We study the density evolution upon isothermal annealing far below the glass transition temperature of various metallic glasses (MGs) with different fragilities. We show that the density variation, which reflects the structural heterogeneity of MGs, has correlations with the Poisson's ratio and the kinetic fragility of their supercooled liquid state. The found relationship between the structure heterogeneity of metallic glasses and dynamic heterogeneity of their supercooled liquids has implications for understanding the structural heterogeneity and heredity, mechanical behaviors, and nature of metallic glass.