Within the Color Glass Condensate (CGC) framework, we compute the cross section for di-jet events in the forward rapidity region in p+p and p+Pb collisions at the LHC. We make use of the recently proposed improved transverse-momentum-dependent (ITMD) factorization formula for forward di-jets, derived from CGC expressions when the jet momenta are much bigger than the saturation scale. This process is nevertheless sensitive to effects of non-linear QCD evolution, when the total transverse momentum of the jet pair is small, and as a direct consequence of those saturation effects, we predict a suppression of the nuclear modification factor for back-to-back jets. We obtain $R_{pPb}\sim 0.5$ for central collisions, and argue that the measurement of the azimuthal angle dependence of the nuclear modifications of forward di-jet events could provide a strong evidence for gluon saturation.