In a recently published work we employ gradient flow on the lattice to extract the leading contribution of the heavy quark momentum diffusion coefficient in the heavy quark limit from calculations of a well-known two-point function of color-electric field operators. In this article we want to report the progress of calculating the recently derived color-magnetic correlator that encodes a finite mass correction to this transport coefficient. The calculations we present here are based on the same ensemble of quenched gauge configurations at $1.5\, T_c$ that we previously used for the color-electric correlator.