  Cygnus X-3 is a high-mass X-ray binary with a compact object accreting matter
from a Wolf-Rayet donor star. Recently, it has been revealed by the Imaging
X-ray Polarimetry Explorer (IXPE) as a hidden Galactic ultra-luminous X-ray
(ULX) source with a luminosity above the Eddington limit along the direction of
a narrow (opening angle <~32 degree) funnel. In between the IXPE observations,
we observed Cyg X-3 with the European VLBI (very long baseline interferometry)
Network at 22 GHz and the NICER X-ray instrument. To probe possible relations
between the X-ray funnel and the potential radio jet from the ULX, we analyzed
the simultaneous multi-wavelength data. Our high-resolution VLBI image reveals
an elongated structure with a position angle of -3.2+/-0.4 degree, accurately
perpendicular to the direction of the linear X-ray polarization. Because Cyg
X-3 was in the radio quiescent state on 2022 November 10, we identify the
mas-scale structure as the innermost radio jet. The finding indicates that the
radio jet propagates along and within the funnel. Moreover, the jet is
marginally resolved in the transverse direction. This possibly results from the
strong stellar winds and the rapid orbital motion of the binary system.
