  Data from the Pierre Auger Observatory are analyzed to search for
anisotropies near the direction of the Galactic Centre at EeV energies. The
exposure of the surface array in this part of the sky is already significantly
larger than that of the fore-runner experiments. Our results do not support
previous findings of localized excesses in the AGASA and SUGAR data. We set an
upper bound on a point-like flux of cosmic rays arriving from the Galactic
Centre which excludes several scenarios predicting sources of EeV neutrons from
Sagittarius $A$. Also the events detected simultaneously by the surface and
fluorescence detectors (the `hybrid' data set), which have better pointing
accuracy but are less numerous than those of the surface array alone, do not
show any significant localized excess from this direction.
