We present the results of a spectroscopic survey performed in the outskirts of the globular cluster NGC 1851 with VIsible MultiObject Spectrograph (VIMOS)/Very Large Telescope (VLT). The radial velocities of 107 stars in a region between 12 and 33 arcmin 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 (σv ≤ 20 km s‑1) peak in the distribution of velocities at vr ˜ 180 km s‑1 constituted mainly by main-sequence stars whose location in the colour-magnitude diagram is compatible with a stream at a similar distance to this cluster. If confirmed, this evidence would strongly support the extragalactic origin of this feature. Based on VIsible MultiObject Spectrograph (VIMOS) observations collected with the Very Large Telescope at the European Southern Observatory, Cerro Paranal, Chile, within the observing programme 082.D-0244.Alexander von Humboldt Fellow for Advanced Research.