The Herschel Space telescope carried out an unprecedented survey of nearby stars for debris discs. The dust present in these debris discs scatters and polarizes stellar light in the visible part of the spectrum. We explore what can be learned with aperture polarimetry and detailed radiative transfer modelling about stellar systems with debris discs. We present a polarimetric survey, with measurements from the literature, of candidate stars observed by DEBRIS and DUNES Herschel surveys. We perform a statistical analysis of the polarimetric data with the detection of far-infrared excess by Herschel and Spitzer with a sample of 223 stars. Monte Carlo simulations were performed to determine the effects of various model parameters on the polarization level and find the mass required for detection with current instruments. Eighteen stars were detected with a polarization 0.01=<P~=3{sigma}P, but only two of them have a debris disc. No statistically significant difference is found between the different groups of stars, with, without, and unknown status for far-infrared excess, and presence of polarization. The simulations show that the integrated polarization is rather small, usually =3{sigma}P)

Cone search capability for table J/MNRAS/483/3510/tablea1 (Polarization data for all the stars observed at OMM and from the Leroy compilation with a polarization P<3{sigma}P)