The inclusive large-pTproduction of a single pion, jet or direct photon, and Drell-Yan processes, are considered for proton-proton collisions in the kinematical range expected for the fixed-target experiment AFTER, proposed at LHC. For all these processes, predictions are given for the transverse single-spin asymmetry,AN, computed according to a Generalised Parton Model previously discussed in the literature and based on TMD factorisation. Comparisons with the results of a collinear twist-3 approach, recently presented, are made and discussed.