While subcortical structures such as the basal ganglia (BG) have been widely explored in relation to motor control, recent evidence suggests that their mechanisms extend to the domain of attentional switching. We here investigated the subcortical involvement in reward related top-down control of visual alpha-band oscillations (8 – 13 Hz), which have been consistently linked to the mechanisms supporting the allocation of visual spatial attention. Given that items associated with contextual saliency (e.g. monetary reward or loss) attract attention, it is not surprising that alpha oscillations are further modulated by the saliency properties of the visual items. The executive network controlling such reward-dependent modulations of oscillatory brain activity has yet to be fully elucidated. Although such network has been explored in terms of cortico-cortical interaction, it likely relies also on the contribution of subcortical regions. To uncover this, we investigated whether derived measures of subcortical structural asymmetries could predict interhemispheric modulation of alpha power during a spatial attention task. We show that volumetric hemispheric lateralization of globus pallidus (GP) and thalamus (Th) explains individual hemispheric biases in the ability to modulate posterior alpha power. Importantly, for the GP, this effect became stronger when the value-saliency parings in the task increased. Our findings suggest that the Th and GP in humans are part of a subcortical executive control network, differently involved in modulating posterior alpha activity. Further investigation aimed at uncovering the interaction between subcortical and neocortical attentional networks would provide useful insight in future studies.