In multi-field reheating after modular j-inflation we investigate the conditions under which baryogenesis via non-thermal leptogenesis can be successfully realized. We introduce three heavy right-handed neutrinos to the non-supersymmetric Standard Model of particle physics, assuming hierarchical neutrino masses. Considering a typical mass for the first right-handed neutrino of the order of $$10^{11}$$ ${10}^{11}$ GeV, suggested from the seesaw mechanism and also from concrete SO(10) grand unification models, we obtain the allowed parameter space for viable baryogenesis. An upper bound for the inflaton mass as well as a lower bound for its branching ratio to the pair of lightest right-handed neutrinos are found and reported.