We investigate the precise location of the radio core in the nearby blazar Mrk 501 for the first time during its X-ray and TeV γ-ray active state in 2012 by revisiting from the perspective of astrometry the six-epoch observations with the Very Long Baseline Array at 43 GHz reported by Koyama et al. We find that the position of the radio core seen at 43 GHz remained stable during our observations from 2012 to 2013 February within 42 μas in the southeast jet direction and 56 μas along the northeast jet direction. This implies that the location of the 43 GHz radio-emitting core was limited within the deprojected scale of 4.6 × 103 Schwarzschild radii (R s) during the high-energy active state. This result is a contrast to another case of the astrometric observation of the famous nearby TeV blazar Mrk 421, which showed a clear radio core position change soon after the large X-ray flare in 2011, reported by Niinuma et al. We compare the two cases and discuss possible origins of the different results of the radio core astrometry in the high-energy active states between the nearby blazars. Based on the internal shock model for blazars, the Lorentz factors of the ejecta explaining the stability of the radio core in Mrk 501 are expected to be a few times smaller than those for the wandering core in Mrk 421.