We have observed a sample of 64 small-diameter sources towards the central -6<l<6, -2<b<2 of the Galaxy with the aim of studying the Faraday rotation measure near the Galactic Centre region. All the sources were observed at 6- and 3.6-cm wavelengths using the ATCA and the VLA. 59 of these sources are inferred to be extragalactic. The observations presented here constitute the first systematic study of the radio polarization properties of the background sources towards this direction and increase the number of known extragalactic radio sources in this part of the sky by almost an order of magnitude. Based on the morphology, spectral indices and lack of polarized emission, we identify four Galactic HII regions in the sample.