We report on Fermi/Large Area Telescope observations of the accreting black hole low-mass X-ray binary V404 Cygni during its outburst in 2015 June–July. Detailed analyses reveal a possible excess of γ-ray emission on 2015 26 June, with a very soft spectrum above 100 MeV, at a position consistent with the direction of V404 Cyg (within the 95 per cent confidence region and a chance probability of 4 × 10−4). This emission cannot be associated with any previously known Fermi source. Its temporal coincidence with the brightest radio and hard X-ray flare in the light curve of V404 Cyg, at the end of the main active phase of its outburst, strengthens the association with V404 Cyg. If the γ-ray emission is associated with V404 Cyg, the simultaneous detection of 511 keV annihilation emission by INTEGRAL reqires that the high-energy γ-rays originate away from the corona, possibly in a Blandford–Znajek jet. The data give support to models involving a magnetically arrested disc where a bright γ-ray jet can re-form after the occurrence of a major transient ejection seen in the radio.