Galaxy clusters represent excellent laboratories to search for axion-like particles (ALPs). They contain magnetic fields which can induce quasi-sinusoidal oscillations in the X-ray spectra of active galactic nuclei situated in or behind them. Due to its excellent energy resolution, the X-ray Integral Field Unit instrument on board the Athena X-ray Observatory will be far more sensitive to ALP-induced modulations than current detectors. As a first analysis of the sensitivity of Athena to the ALP–photon coupling gaγγ, we simulate observations of the Seyfert galaxy NGC 1275 (hosting the radio source 3C 84) in the Perseus cluster using the SIXTE simulation software. We estimate that for a 200 ks exposure, a non-observation of spectral modulations will constrain gaγγ ≲ 1.5 × 10^-13 GeV^-1 for ma ≲ 10− 12 eV, representing an order of magnitude improvement over constraints derived using the current generation of satellites.