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We apply the $k_T$-factorization approach to the production of $\phi$ mesonin deep-inelastic scattering. The helicity-conserving $\gamma^*(T,L) \to \phi$impact factor is calculated for longitudinal and transverse photon polarizationusing $\phi$ meson distribution amplitudes. Different unintegrated gluondistributions are used in the calculations. The formalism for masslessquarks/antiquarks gives too large transverse and longitudinal cross sectionsfor photon virtualities below $Q^2\sim 8 \, \rm{GeV}^2$. We suggest how toimprove the description of the HERA data by introducing effective strange quarkmasses into the formalism. We derive the corresponding massive impact factor bycomparing to the light-cone wave function representation used in previous$k_T$-factorization calculations and the color-dipole approaches. As abyproduct we present expressions for higher twist-amplitudes as weightedintegrals over the light-cone wave function. The quark mass $m_q \approx 0.5$GeV allows to improve the description of both longitudinal and transverse crosssection down to $Q^2 \sim$ 4 GeV$^2$. We present also the polarized crosssection ratio $\sigma_L/\sigma_T$ and the behavior of the total cross section$\sigma_{tot} = \sigma_{L} + \sigma_{T}$ as a function of photon virtuality.

Exclusive production of $\phi$ meson in the $\gamma^*\,p \to \phi\,p$ reaction at large photon virtualities within $k_T$-factorization approach