We report on the detailed radio status of the M87 jet during the Very-High-Energy (VHE) gamma-ray flaring event in April 2010, obtained from high-resolution, multi-frequency, phase-referencing VLBA observations. We especially focus on the properties for the jet base (the radio core) and the peculiar knot HST-1, which are currently favored as the gamma-ray emitting sites. During the VHE flaring event, the HST-1 region remains stable in terms of its structure and flux density in the optically thin regime above 2GHz, being consistent with no signs of enhanced activities reported at X-ray for this feature. The radio core shows an inverted spectrum at least up to 43GHz during this event. Astrometry of the core position, which is specified as ~20Rs from the central engine in our previous study, shows that the core position is stable on a level of 4Rs. The core at 43 and 22GHz tends to show slightly (~10%) higher flux level near the date of the VHE flux peak compared with the epochs before/after the event. The size of the 43-GHz core is estimated to be ~17Rs, which is close to the size of the emitting region suggested from the observed time scale of rapid variability at VHE. These results tend to favor the scenario that the VHE gamma-ray flare in 2010 April is associated with the radio core.