Forward Drell-Yan production at high energy can provide important constraints on gluon densities at small x, in the saturation regime. In this work, we focus on the nuclear modification of this process, which could be measured at the LHC in the near future. For this, we employ the color dipole approach, using the optical Glauber model to relate the dipole cross section of a nucleus to the one of a proton. Combining these results with our earlier results for forward J=ψ production, we compute the ratio of the nuclear modification factors of these two processes. This observable was recently suggested as a way to distinguish between initial and final state effects in forward particle production.