Is there a nearby microlensing stellar remnant hiding in Gaia DR3 astrometry?

Massive galactic lenses with large Einstein Radii should cause a measurable astrometric microlensing effect, i.e. the light centroid shift due to the motion of the two images. Such a shift in the position of a background star due to microlensing was not included in the $Gaia$ astrometric model, therefore significant deviation should cause $Gaia$'s astrometric parameters to be determined incorrectly. Here we studied one of the photometric microlensing events reported in the $Gaia$ DR3, GaiaDR3-ULENS-001, for which poor goodness of $Gaia$ fit and erroneous parallax could indicate the presence of the astrometric microlensing signal. Based on the photometric microlensing model, we simulated $Gaia$ astrometric time-series with the astrometric microlensing effect added. We found that including microlensing with the angular Einstein Radius of $\theta_{\rm E}$ = $2.60^{+0.21}_{-0.24}$ mas ($2.47^{+0.28}_{-0.24}$ mas) assuming positive (negative) impact parameter $u_0$ reproduces well the astrometric quantitie reported by $Gaia$. We estimate the mass of the lens to $1.00^{+0.23}_{-0.18}$ $M_\odot$ ($0.70^{+0.17}_{-0.13}$ $M_\odot$) and its distance to $0.90^{+0.14}_{-0.11}$ kpc ($0.69^{+0.13}_{-0.09}$ kpc), proposing the lens could be a nearby isolated white dwarf.