Molecular dynamics simulations of diffusion of isolated tagged spheres in liquid crystalline molecules have been carried out. While the diffusion is isotropic at density slightly below the isotropic-nematic phase transition, it is found to become strongly anisotropic very close to the I-N transition where the diffusion perpendicular to the direction of the order parameter g(D-perpendicular to) decouples from the parallel (D-parallel to) component. The diffusion coefficient of the sphere also shows a marked slowing down as the I-N transition approaches, in accordance with the mode coupling theory analysis. The variation of the orientational order parameter with the density shows a sharp transition at a reduced density, rho (*)(IN) where plot of the ratio, D-parallel to/D-perpendicular to against the reduced density, rho (*) clearly shows the emergence of anisotropy. D-perpendicular to could be fitted to a form (rho (*)(c)-rho (*))(p) with a rho (*)(c) which is slightly larger than rho (*)(IN). The diffusion shows a strong non-Stokesian dependence on the radius of the spheres, in agreement with recent experiments.