By considering three virtual gravitational constants assumed to be associated with gravitational, electromagnetic and strong interactions, Fermi’s weak coupling constant can be shown to be a natural manifestation of microscopic quantum gravity. As our approach is heuristic and completely different from the current methods of estimating the Newtonian gravitational constant, concerning the call of ‘Ideas lab 2016’ organized by NSF, we appeal for inclusion of this theoretical work as a project under the unification scheme. Estimated magnitudes of Fermi’s weak coupling constant and Newtonian gravitational constant are 1.44021X10(-62) J.m3 and 6.679856X10(-11) m3/kg/sec2 respectively.