We studied a system of a core-shell nanowire array in the liquid crystal (LC) matrix 5CB supposing that the nanowire shell permittivity is anisotropic with radially power-law dependent components. The nanowire core material is either silver or gold. We calculated the effective permittivity tensor of the core-shell nanowire array in the LC matrix, and show that the system under consideration can possess two hyperbolic metamaterial (HMM) areas: where the real part of the effective permittivity component parallel to the nanowire is negative, and the real part of the effective permittivity component perpendicular to the nanowire is negative. Dependence of the frequency position for these areas on the core-shell nanowire parameters and the LC matrix orientational state is studied.