In this paper we present a comprehensive analysis of the exclusive heavy quark photoproduction in pp, pPb and PbPb collisions at LHC and FCC energies using the color dipole formalism and taking into account of nonlinear corrections to the QCD dynamics. We estimate the rapidity distributions and cross sections for the charm and bottom production considering three phenomenological models for the dipole-proton scattering amplitude that are able to describe the ep HERA data. Our results indicate that a future experimental analysis of this process is feasible, which will allow us to improve our understanding of the QCD dynamics.