M87 has been identified as a displaced supermassive black hole (SMBH) candidate. We investigated this possibility by a temporal analysis of 12 adaptive-optics assisted VLT and HST images spanning 20 yr. We found that the centre of the isophotal fitting to the nuclear region of M87 - assumed to mark the centre of mass of the galaxy - changes location depending on the image and size of the image analysed. In an absolute frame of reference, the change varies from 15 to 130 miliarcseconds (mas) with respect to the active galactic nucleus (AGN), which remains stable within an uncertainty of ±15 mas in both x- and y-axis. The temporal analysis of the results indicates that the major displacements measured coincide with a powerful outburst that took place between 2003 and 2007, where there was a flux increment in the nucleus and the first knot of the jet. After the outburst, the isophotal centre remains stable and is consistent with the AGN location. This suggests that the displacements are artificially caused by a flux variation in the galaxy and that the SMBH actually resides in the equilibrium position. We caution about the determination of the galaxy photocentre by isophotal fitting in cases of nuclear variability and/or presence of photometric irregularities, and advise a long-term temporal analysis of the results to confirm possible displaced SMBHs.