The timing of slow auditory cortical activity aligns to the rhythmic fluctuations in speech. This entrainment is considered to be a marker of the prosodic and syllabic encoding of speech, and has been shown to correlate with intelligibility. Yet, whether and how auditory cortical entrainment is influenced by the activity in other speech–relevant areas remains unknown. Using source-localized MEG data, we quantified the dependency of auditory entrainment on the state of oscillatory activity in fronto-parietal regions. We found that delta band entrainment interacted with the oscillatory activity in three distinct networks. First, entrainment in the left anterior superior temporal gyrus (STG) was modulated by beta power in orbitofrontal areas, possibly reflecting predictive top-down modulations of auditory encoding. Second, entrainment in the left Heschl's Gyrus and anterior STG was dependent on alpha power in central areas, in line with the importance of motor structures for phonological analysis. And third, entrainment in the right posterior STG modulated theta power in parietal areas, consistent with the engagement of semantic memory. These results illustrate the topographical network interactions of auditory delta entrainment and reveal distinct cross-frequency mechanisms by which entrainment can interact with different cognitive processes underlying speech perception.