  The production of forward $J/\psi$ mesons in proton-nucleus collisions can
provide important information on gluon saturation. In a previous work we
studied this process in the Color Glass Condensate framework, describing the
target using a dipole cross section fitted to HERA inclusive data and
extrapolated to the case of a nuclear target using the optical Glauber model.
In this work we study the centrality dependence of the nuclear suppression in
this model and compare our results with recent LHC data for this observable.
