We present a survey of RR Lyrae stars in an area of 50 deg(2) around the globular cluster omega Centauri, aimed at detecting debris material from the alleged progenitor galaxy of the cluster. We detected 48 RR Lyrae stars, only 11 of which have been previously reported. Ten of the eleven previously known stars were found inside the tidal radius of the cluster. The rest were located outside the tidal radius up to distances of similar to 6 degrees from the center of the cluster. Several of these stars are located at distances similar to that of omega Centauri. We investigate the probability that they may have been stripped off the cluster. To do this, we studied their properties (mean periods) by calculating the expected halo and thick-disk population of RR Lyrae stars in this part of the sky, analyzing the radial velocity of a sub-sample of the RR Lyrae stars, and finally, studying the probable orbits of this sub-sample around the Galaxy. The results of these investigations do not support the scenario that there is significant tidal debris around omega Centauri, which confirms previous studies on the region. It is puzzling that tidal debris has been found elsewhere but not near the cluster itself.