  We cross correlate Gamma--Ray Bursts and X--Ray selected clusters of galaxies
at z\leq0.45. We find a positive 2\sigma signal for the angular
cross--correlation function w_{bc}(\theta) on scales \theta\leq 3 deg between
short GRBs and clusters. Conversely, no correlation is found between clusters
and the population of long GRBs. The comparison with the cluster
autocorrelation function shows that short GRBs do not trace the cluster
distribution as not all short GRBs are found in clusters. A higher signal in
w_{bc}(\theta) is found if we only consider the cluster population up to z=0.1.
By comparing the short burst autocorrelation function with model predictions we
then constrain short bursts to mostly originate within \sim 270 Mpc (i.e. z\leq
0.06). Our analysis also reveals that short GRBs are better correlated with
``normal'' galaxies. The double compact object merger model for short GRBs
would associate them preferentially to early--type galaxies but the present
statistics do not allow us to exclude that at least a fraction of these events
might also take place in late--type galaxies, in agreement with recent
evidences.
