A mean field theory is introduced to describe the phase separations in binary mixtures of a liquid crystal and a non-nematic polymer which means that nematic ordering is forbidden in the constituent pure polymers. The theory takes into account the partial orientational ordering of the polymer chain induced by the liquid crystal solvents. We predict that a triple point and a new stable nematic phase can be induced by the anisotropic coupling between the polymer and the liquid crystal. The new types of induced nematic phases are examined with respect to their dependence on polymer molecular weight and stiffness.