We discuss gluon-gluon mechanisms for production of mesons with hidden strangeness, such as η ′ and φ meson, in proton-proton collisions at large energies. The g * g * → η ′ and g * g * → φg mechanisms are considered only and the corresponding cross sections are calculated in the k t -factorization approach. The F γ * γ * →η ′ and F g * g * →η ′ form factors are calculated from quarkantiquark η ′ light-cone wave function including quark/antiquark transverse momenta. The result for two-photon transition form factor demonstrates that higher twists may survive even to large photon virtualities. The result is compared with the result of a recent leading-twist NLO analysis which uses phenomenological distribution amplitudes fitted to exclusive production of η ′ in e + e − → e + e − η ′ reaction. We calculate transverse momentum distributions of both η ′ and φ mesons in proton-proton collisions for RHIC and LHC energies. The results are compared to experimental data whenever available. The results of the Lund string model are shown for comparison for η ′ production at LHC energies. It seems that the two-gluon fusion is not the dominant mechanism for both φ and η ′ production, although the situation for η ′ , especially at larger energies, is less clear due to lack of experimental data.