Recent evidence suggests that visuospatial attentional performance is not stable over time but fluctuates in a rhythmic fashion. These attentional rhythms allow for sampling of different visuospatial locations in each cycle of this rhythm. However, it is still unclear in which paradigmatic circumstances rhythmic attention becomes evident. First, it is unclear at what spatial locations rhythmic attention occurs. Second, it is unclear how the behavioural relevance of each spatial location determines the rhythmic sampling patterns. Here, we aim to elucidate these two issues. Firstly, we aim to find evidence of rhythmic attention at the predicted (i.e. cued) location under moderately informative predictor value, replicating earlier studies. Secondly, we hypothesise that rhythmic attentional sampling behaviour will be affected by the behavioural relevance of the sampled location, ranging from non-informative to fully informative. To these aims, we used a modified Egly-Driver task with three conditions: a fully informative cue, a moderately informative cue (replication condition), and a non-informative cue. We did not find evidence of rhythmic sampling at cued locations, failing to replicate earlier studies. Nor did we find differences in rhythmic sampling under different predictive values of the cue. The current data does not allow for robust conclusions regarding the non-cued locations due to the absence of a priori hypotheses. Post-hoc explorative data analyses, however, clearly indicate that attention samples non-cued locations in a theta-rhythmic manner, specifically when the cued location bears higher behavioural relevance than the non-cued locations.