We discuss structural and kinematical properties of the stellar halo and the old globular cluster system (GCS) in the Large Magellanic Cloud (LMC) based on numerical simulations of the LMC formation. We particularly discuss the observed possible GCS's rotational kinematics (V/sigma > 2) that appears to be significantly different from the stellar halo's one with a large velocity dispersion (~50 km/s). We consider that both halo field stars and old GCs can originate from low-mass subhalos virialized at high redshifts (z >6). We investigate the final dynamical properties of the two old components in the LMC's halo formed from merging of low-mass subhalos with field stars and GCs. We find that the GCS composed of old globular clusters (GCs) formed at high redshifts (z > 6) has little rotation (V/sigma ~0.4) and structure and kinematics similar to those of the stellar halo. This inconsistency between the simulated GCS's kinematics and the observed one is found to be seen in models with different parameters. This inconsistency therefore implies that if old, metal-poor GCs in the LMC have rotational kinematics, they are highly unlikely to originate from the low-mass subhalos that formed the stellar halo. We thus discuss a scenario in which the stellar halo was formed from low-mass subhalos with no/few GCs whereas the GCS was formed at the very early epoch of the LMC's disk formation via dissipative minor and major merging of gas-rich subhalos and gas infall. We suggest that there can be a threshold subhalo mass above which GCs can be formed within subhalos at high redshifts and thus that this threshold causes differences in physical properties between stellar halos and GCSs in less luminous galaxies like the LMC. ; Comment: 10 pages, 8 figures, accepted by MNRAS