Context. The detection or absence of a polarisation signal in the diffuse interstellar band (DIB) profile can possibly give important clues on the identity of its carrier. For molecular gas-phase carriers the effect of polarisation on its electronic transitions depends, although uncertain how exactly, on its physical properties (e.g. molecular structure). On the other hand, if the carriers are grains, impurities or defects in grain mantles are also expected to show up in the polarisation of DIBs.