We present estimates of transverse single spin asymmetry (TSSA) in within the colour evaporation model of charmonium production in a generalized parton model (GPM) framework, using the recently obtained best fit parameters for the gluon Sivers function (GSF) extracted from PHENIX data on TSSA in at midrapidity. We calculate asymmetry at GeV, and compare the results with PHENIX data on TSSA in the process . We also present estimates for asymmetry at GeV corresponding to the proposed fixed target experiment AFTER@LHC and at GeV corresponding to the higher RHIC energy. Finally, we investigate the effect of the transverse momentum dependent (TMD) evolution of the densities involved, on the asymmetry.