We present preliminary results for the charm
quark mass in the $N_f=4$ RGI scheme. These were
obtained using $N_f=2+1$ CLS ensembles with $\mathcal{O}(a)$
non-perturbatively improved Wilson fermions. We employed
five different lattice spacings, ranging down to $a\lesssim 0.04$~fm
and realized
approximately physical pion and kaon masses, with ensembles spread out
along three different trajectories in the quark mass plane, enabling
a thorough study of the dependence on the lattice spacing and the
light and strange sea quark masses. We sketch our analysis
strategy and find that the dominant errors at present
are due to the renormalization and scale setting uncertainties.