Using classical density functional theory, the forces between two cylindrical nanoparticles in a liquid crystal solvent are calculated. Both the nematic and isotropic phases of the solvent are considered. In the nematic phase, the interaction is highly anisotropic. At short range, changes in the defect structure around the cylinders leads to a complex interaction between them. In the isotropic phase, an attractive interaction arises due to overlap between halos of ordered fluid adsorbed on the surfaces of the cylinders.