Covert speech involves the internal generation of articulatory movements and their sensory consequences. While overt speech involves a combination of feedforward and feedback signals, feedback signals may be substantially different, or even absent, during covert speech. Despite the differences, we conjectured that sensorimotor interareal communication during covert speech is implemented through the same channels recruited during overt speech. An influential overt speech model proposed that feedforward and feedback signals are segregated to the left and right hemispheres, respectively. Here, we used magnetoencephalography to investigate the lateralization of functional connectivity before and after covert speech production. The data reveal leftward lateralization preceding and rightward lateralization following predicted covert speech onset. This alternating lateralization pattern is observed only in the connection between premotor and auditory regions and in the alpha frequency band. The electrophysiological data, derived entirely from covert speech, add a provocative perspective to adjudicate between overt speech motor control models.