Observed HI accretion around nearby galaxies can only account for a fraction of the gas supply needed to sustain the currently observed star formation rates. It is possible that additional accretion happens in the form of low column density cold flows, as predicted by numerical simulations of galaxy formation. To contrain the presence and properties of such flows, we present deep HI observations obtained with the NRAO Green Bank Telescope of an area measuring 4 by 4 degrees around NGC 2403. These observations, with a 5{sigma} detection limit of 2.4x10^18^cm^-2^ over a 20km/s linewidth, reveal the presence of a low-column density, extended cloud outside the main HI disk, about 17' (~16kpc or ~2R_25_) to the NW of the center of the galaxy. The total HI mass of the cloud is 6.3x10^6^M_{sun}_, or 0.15% of the total HI mass of NGC 2403. The cloud is associated with an 8kpc anomalous-velocity HI filament in the inner disk, previously observed in deep VLA observations by Fraternali et al. (2001ApJ...562L..47F, 2002AJ....123.3124F). We discuss several scenarios for the origin of the cloud, and conclude that it is either accreting from the intergalactic medium, or is the result of a minor interaction with a neigbouring dwarf galaxy.