ABSTRACT Sulphur depletion in the interstellar medium (ISM) is a long-standing issue, as only 1 per cent of its cosmic abundance is detected in dense molecular clouds (MCs), while it does not appear to be depleted in other environments. In addition to gas phase species, MCs also contain interstellar dust grains, which are irregular, micron-sized, solid aggregates of carbonaceous materials, and/or silicates. Grains provide a surface where species can meet, accrete, and react. Although freeze-out of sulphur on to dust grains could explain its depletion, only OCS and, tentatively, SO2 were observed on their surfaces. Therefore, it is our aim to investigate the interaction between sulphur-containing species and the exposed mineral core of the grains at a stage prior to when sulphur depletion is observed. Here, the grain core is represented by olivine nanoclusters, one of the most abundant minerals in the ISM, with composition Mg4Si2O8 and Mg3FeSi2O8. We performed a series of quantum mechanical calculations to characterize the adsorption of nine S-bearing species, both neutral and charged, on to the nanoclusters. Our calculations reveal that the Fe–S interaction is preferred to Mg–S, causing sometimes the chemisorption of the adsorbate. These species are more strongly adsorbed on the bare dust grain silicate cores than on water ice mantles, and hence therefore likely sticking on the surface of grains forming part of the grain core. This demonstrates that the interaction of bare grains with sulphur species in cloud envelopes can determine the S-depletion observed in dense molecular clouds.