  We study the consistency of dynamical fermionic matter with the asymptotic
safety scenario of quantum gravity using the functional renormalisation group.
Since this scenario suggests strongly coupled quantum gravity in the UV, one
expects gravity-induced fermion self-interactions at energies of the
Planck-scale. These could lead to chiral symmetry breaking at very high
energies and thus to large fermion masses in the IR. The present analysis which
is based on the previous works \cite{Christiansen:2015rva, Meibohm:2015twa},
concludes that gravity-induced chiral symmetry breaking at the Planck scale is
avoided for a general class of NJL-type models, regardless of the number of
fermion flavours. This suggests that the phase diagram for these models is
topologically stable under the influence of gravitational interactions.
