Selective routing of information between cortical areas is required in order to combine different sources of information according to cognitive demand. Recent experiments have suggested that alpha band activity originating from the pulvinar coordinates this inter-areal cortical communication. Using a computer model we investigated whether top-down induced shifts in the relative alpha phase between two cortical areas could modulate cortical communication, quantified in terms of changes in gamma band coherence between them. The network model was comprised of two uni-directionally connected neuronal populations of spiking neurons, each representing a cortical area. We find that the phase difference of the alpha oscillations modulating the two neuronal populations strongly affected the interregional gamma-band neuronal coherence. We confirmed that a higher gamma band coherence also resulted in more efficient transmission of spiking information between cortical areas, thereby confirming the value of gamma coherence as a proxy for cortical information transmission. In a model where both neuronal populations were connected bi-directionally, the relative alpha phase determined the directionality of communication between the populations. Our results show the feasibility of a physiological realistic mechanism for routing information in the brain based on coupled oscillations. Our model results in a set of testable predictions regarding phase shifts in alpha oscillations under different task demands requiring experimental quantification of neuronal oscillations in different regions in e.g. attention paradigms.