  We consider light-fermion three-loop corrections to $gg\to HH$ using forward
scattering kinematics in the limit of a vanishing Higgs boson mass, which
covers a large part of the physical phase space. We compute the form factors
and discuss the technical challenges. The approach outlined in this letter can
be used to obtain the full virtual corrections to $gg\to HH$ at
next-to-next-to-leading order.
