Context. Proxima Centauri is the closest star to the Sun and it 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. Aims. While identification of the optical counterpart of this planet is expected to be very difficult, successful identification would allow for a detailed characterization of the closest planetary system. Methods. We searched for a counterpart in SPHERE images acquired over four years through the SHINE survey. In order to account for the expected 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, called K-stacker. Results. We did not obtain a clear detection. The best candidate has signal-to-noise ratio (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 the distribution of noise is uniform over the image, a fact that is likely not true. The position of this candidate and the orientation of its orbital plane fit well with observations in the ALMA 12 m array image. However, the astrometric signal expected from the orbit of the candidate we detected is 3σ 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. Conclusions. On the other hand, if confirmed, this would be the first observation in imaging of a planet discovered from radial velocities and the second planet (after Fomalhaut b) of reflecting circumplanetary material. Further confirmation observations should be done as soon as possible.