The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron–hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb–Pb and p–Pb collisions at √sNN = 39 and 63 TeV, respectively, per nucleon–nucleon collision, with integrated luminosities above 30 nb−1 per month for Pb–Pb. This is a report by the working group on heavy-ion physics of the FCC Study. First ideas on the physics opportunities with heavy ions at the FCC are presented, covering the physics of the Quark–Gluon Plasma, of gluon saturation, of photon-induced collisions, as well as connections with other fields of high-energy physics.