We have observed a sample of 64 small diameter sources towards the central -6 degree < l< 6 degree, -2 degree < b < 2 degree of the Galaxy with the aim of studying the Faraday rotation measure near the Galactic Centre (GC) region. All the sources were observed at 6 and 3.6 cm wavelengths using the ATCA and the VLA. Fifty nine of these sources are inferred to be extragalactic. The observations presented here constitute the first systematic study of the radio polarisation properties of the background sources towards this direction and increases 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 polarised emission, we identify four Galactic HII regions in the sample.