  The nuclear suppression of forward $J/\psi$ production in high energy
proton-nucleus collisions can be used as a probe of gluon saturation at small
$x$. In an earlier work we studied this suppression in minimum bias collisions
in the Color Glass Condensate formalism, relying on the optical Glauber model
to obtain the dipole cross section of the nucleus from the one of the proton
fitted to HERA DIS data. Here we study how the impact parameter dependence of
this model can be used to compare our results with recent LHC data on the
centrality dependence of this suppression.
