  The ESS$\nu$SB project is a proposed neutrino oscillation experiment based on
the European Spallation Source with the search for leptonic CP 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 $\sin^2(2\theta_{\mu e}) \simeq
2(8)\cdot 10^{-3}$ at $5\sigma$ assuming 15% bin-to-bin (un)correlated
systematics.
