  The X-ray source CXO\, J085201.4$-$461753in the few kyr-old Vela Jr.
supernova remnant (G266.2-1.2) belongs to the peculiar class of isolated
neutron stars dubbed "Central Compact Objects" (CCOs). At variance with the
other CCOs, which are only detected in the X-rays, \cxo\ has been possibly
detected also at other wavelengths. In particular, a candidate near-infrared
counterpart (H = 21.6 $\pm$0.1) was detected by the Very Large Telescope (VLT)
in addition to a 6\arcsec-wide nebula detected in H$\alpha$, interpreted as a
velocity-driven bow-shock. Here, we present new near-infrared and optical VLT
observations of the candidate counterpart to \cxo\ and its nebula to confirm
the proposed associations. Moreover, we used archival Chandra observations to
measure for the first time the CXO\, J085201.4$-$461753 proper motion. The
comparison between the two sets of near-infrared VLT images, taken 10.56 year
apart, do not show evidence of proper motion for the candidate counterpart to
CXO\, J085201.4$-$461753, expected from its 4\arcmin\ offset from the SNR
geometrical centre, with a $3\sigma$ upper limit of $\sim 10$ mas yr$^{-1}$.
This is much smaller than the expected proper motion of $\sim$50--100 mas
yr$^{-1}$, which, in turn, is below the $3\sigma$ upper limit of $\sim$ 300 mas
yr$^{-1}$ that we obtained with Chandra. At the same time, VLT spectroscopy
resolved the nebula optical emission, which is dominated by the NII doublet at
6548 and 6584 \AA\ and not by H$\alpha$. To summarise, we conclude that the
proposed near-infrared counterpart is likely unassociated with \cxo\ and that
the nebula is not a velocity-driven bow-shock.
