We present the results of a spectroscopic survey performed in the outskirts of the globular cluster NGC1851 with VIMOS@VLT. The radial velocities of 107 stars in a region between 12 and 33 around the cluster have been derived. We clearly identify the cluster stellar population over the entire field of view, indicating the presence of a significant fraction of stars outside the tidal radius predicted by King models. We also find tentative evidence of a cold (sigma_v< 20 km/s) peak in the distribution of velocities at v_r~180 km/s constituted mainly by Main Sequence stars whose location in the color-magnitude diagram is compatible with a stream at a similar distance of this cluster. If confirmed, this evidence would strongly support the extra-Galactic origin of this feature.