It is well established that magnetars are neutron stars with extreme magnetic fields and young ages, but the evolutionary pathways to their creation are still uncertain. Since most massive stars are in binaries, if magnetars are a frequent result of core-collapse supernovae, some fraction are expected to have a bound companion at the time of observation. In this paper, we utilize literature constraints, including deep Hubble Space Telescope imaging, to search for bound stellar companions to magnetars. The magnitude and colour measurements are interpreted in the context of binary population synthesis predictions. We find two candidates for stellar companions associated with CXOU J171405.7–381031 and SGR 0755–2933, based on their J-H colours and H-band absolute magnitudes. Overall, the proportion of the Galactic magnetar population with a plausibly stellar near-infrared counterpart candidate, based on their magnitudes and colours, is between 5 and 10 per cent. This is consistent with a population synthesis prediction of 5 per cent, for the fraction of core-collapse neutron stars arising from primaries which remain bound to their companion after the supernova. These results are therefore consistent with magnetars being drawn in an unbiased way from the natal core-collapse neutron star population, but some contribution from alternative progenitor channels cannot be ruled out.