  Proxima Centauri is known to host an earth-like planet in its habitable zone;
very recently a second candidate planet was proposed based on radial
velocities. At quadrature, the expected projected separation of this new
candidate is larger than 1 arcsec, making it a potentially interesting target
for direct imaging. While difficult, identification of the optical counterpart
of this planet would allow detailed characterization of the closest planetary
system. We searched for a counterpart in SPHERE images acquired during four
years through the SHINE survey. In order to account for the large orbital
motion of the planet, we used a method that assumes the circular orbit obtained
from radial velocities and exploits the sequence of observations acquired close
to quadrature in the orbit. We checked this with a more general approach that
considers keplerian motion, K-stacker. We did not obtain a clear detection. The
best candidate has S/N=6.1 in the combined image. A statistical test suggests
that the probability that this detection is due to random fluctuation of noise
is < 1% but this result depends on the assumption that distribution of noise is
uniform over the image. The position of this candidate and the orientation of
its orbital plane fit well with observations in the ALMA 12m array image.
However, the astrometric signal expected from the orbit of the candidate we
detected is 3-sigma away from the astrometric motion of Proxima as measured
from early Gaia data. This, together with the unexpectedly high flux associated
with our direct imaging detection, means we cannot confirm that our candidate
is indeed Proxima c. On the other hand, if confirmed, this would be the first
observation in imaging of a planet discovered from radial velocities and the
second one (after Fomalhaut b) of reflecting circumplanetary material. Further
confirmation observations should be done as soon as possible.
