The ESS nu SB project is a proposed neutrino oscillation experiment based on the European Spallation Source with the search for leptonic CP violation as its main aim. In this letter we show that a near detector at around 1 km distance from the beamline is not only very desirable for keeping the systematic errors affecting the CP search under control, but would also provide a significant sensitivity probe for sterile neutrino oscillations in the region of the parameter space favored by the long-standing LSND anomaly. We find that the effective mixing angle theta(mu e) can be probed down to sin(2)(2 theta(mu e)) similar or equal to 2(8) . 10(-3) at 5 sigma assuming 15% bin-to-bin (un) correlated systematics.