We report on Fermi/Large Area Telescope observations of the accreting black hole low-mass X-ray binary V404 Cygni during its outburst in June-July 2015. Detailed analyses reveal a possible excess of $γ$-ray emission on 26 June 2015, with a very soft spectrum above $100$ MeV, at a position consistent with the direction of V404 Cyg (within the $95\%$ confidence region and a chance probability of $4 \times 10^{-4}$). 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 lightcurve 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 requires 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 disk where a bright $γ$-ray jet can re-form after the occurrence of a major transient ejection seen in the radio. ; Comment: 5 pages, 3 figures, accepted for publication in MNRAS