The inclusion of top-quark-mass effects in the NNLO QCD corrections to $gg \to HH$ is desirable
due to the significant impact of the top-mass renormalization scheme uncertainty observed at
NLO. In these proceedings, we report on the calculation of a subset of diagrams contributing
to the virtual NNLO QCD corrections to $gg \to HH$. These diagrams, in which the two Higgs
bosons couple to two independent top-quark loops, are computed using asymptotic expansions in
the forward limit.

