Injection of liquid foam through soils is increasingly used in applications such as soil remediation or soil improvement, where it is also crucial to control the liquid relative permeability through the foam-filled soil. We have measured the time dependence of the liquid permeability of granular packings initially filled with liquid foam for different values of the liquid saturation. It is shown that, systematically, permeability increases significantly over time before reaching saturation. We have demonstrated that this evolution is directly related to the coarsening of the liquid foam confined in the pore space. We have shown how the evolution of the liquid permeability can be predicted from the knowledge of the bubble size evolution