We study the associated J∕ψ and direct photon production in the high-energy factorization, as it is formulated in the parton Reggeization approach, using two different models for the hadronization of a heavy quark–antiquark pair into a heavy quarkonium, namely the nonrelativistic quantum chromodynamics (NRQCD) and the improved color evaporation model (ICEM). We find essential differences in the predictions for cross-sections and transverse momenta spectra obtained using the NRQCD and the ICEM, which can be used to discriminate between these models. Our prediction for cross-sections of the associated J∕ψ and direct photon production at the LHC energies slightly overestimates the results obtained earlier in the next-to-leading order (NLO) calculation in the collinear parton model (CPM). We predict different two-particle correlation spectra in the associated J∕ψ and direct photon production, which may be of interest for experimental study.