Context. X-ray observations performed with the Röntgen Satellite (ROSAT) led to the discovery of seven radio-silent isolated neutron stars (INSs) which are detected only through the relatively dim and purely thermal X-ray emission from the cooling star surface. A few of these INSs (X-ray Dim INSs, or XDINSs) have been also detected at optical wavelengths where they seem to feature thermal spectra. Optical studies of XDINSs thus play a crucial role in mapping the temperature distribution on the neutron star surface and in investigating the existence of an atmosphere around the neutron star. Aims. The aim of this work is to investigate the optical identification of the XDINS RX J0420.0−5022, tentatively proposed in the literature based on Very Large Telescope (VLT) observations. Methods. We re-analysed the original VLT observations of the proposed counterpart to assess its detection significance and we performed deeper VLT observations aiming at a higher confidence detection. Results. With a ∼2σ detection significance and a re-computed flux of B = 27.52 ± 0.61, we cannot rule out that the proposed counterpart was spurious and produced by the halo of a very bright nearby star. While we could not detect the proposed counterpart in our deeper VLT observations, we found evidence for a marginally significant (∼3.9σ) detection of a similarly faint object (B = 27.5 ± 0.3), ≈0. 5 north of it and coincident with the updated Chandra position of RX J0420.0−5022. Interestingly, the angular separation is consistent with the upper limit on the RX J0420.0−5022 proper motion, which suggests that we might have actually detected the originally proposed counterpart. From the flux of the putative RX J0420.0−5022 counterpart we can rule out a >7 optical excess with respect to the extrapolation of the XMM-Newton spectrum. Conclusions. High spatial resolution observations with the refurbished Hubble Space Telescope (HST) are the only way to confirm the detection of the putative candidate counterpart and to validate its identification with RX J0420.0−5022.