Frequency tagging of sensory inputs (presenting stimuli that fluctuate periodically at rates to which the cortex can phase lock) has been used to study attentional modulation of neural responses to inputs in different sensory modalities. For visual inputs, the visual steady-state response (VSSR) at the frequency modulating an attended object is enhanced, while the VSSR to a distracting object is suppressed. In contrast, the effect of attention on the auditory steady-state response (ASSR) is inconsistent across studies. However, most auditory studies analyzed results at the sensor level or used only a small number of equivalent current dipoles to fit cortical responses. In addition, most studies of auditory spatial attention used dichotic stimuli (independent signals at the ears) rather than more natural, binaural stimuli. Here, we asked whether these methodological choices help explain discrepant results. Listeners attended to one of two competing speech streams, one simulated from the left and one from the right, that were modulated at different frequencies. Using distributed source modeling of magnetoencephalography results, we estimate how spatially directed attention modulates the ASSR in neural regions across the whole brain. Attention enhances the ASSR power at the frequency of the attended stream in contralateral auditory cortex. The attended-stream modulation frequency also drives phase-locked responses in the left (but not right) precentral sulcus (lPCS), a region implicated in control of eye gaze and visual spatial attention. Importantly, this region shows no phase locking to the distracting stream. Results suggest that the lPCS in engaged in an attention-specific manner. Modeling results that take account of the geometry and phases of the cortical sources phase locked to the two streams (including hemispheric asymmetry of lPCS activity) help to explain why past ASSR studies of auditory spatial attention yield seemingly contradictory results.