Oral communication regularly takes place amidst background noise, requiring the ability to selectively attend to a target speech stream. Musical training has been shown to be beneficial for this task. Regarding the underlying neural mechanisms, recent studies showed that the speech envelope is tracked by neural activity in auditory cortex, which plays a role in the neural processing of speech, including speech in noise. The neural tracking occurs predominantly in two frequency bands, the delta and the theta bands. However, much regarding the specifics of these neural responses, as well as their modulation through musical training, still remain unclear. Here, we investigated the delta- and theta-band cortical tracking of the speech envelope of target and distractor speech using magnetoencephalography (MEG) recordings. We thereby assessed both musicians and nonmusicians to explore potential differences between these groups. The cortical speech tracking was quantified through source-reconstructing the MEG data and subsequently relating the speech envelope in a certain frequency band to the MEG data using linear models. We thereby found the theta-band tracking to be dominated by early responses with comparable magnitudes for target and distractor speech, whereas the delta band tracking exhibited both earlier and later responses that were modulated by selective attention. Almost no significant differences emerged in the neural responses between musicians and nonmusicians. Our findings show that only the speech tracking in the delta but not in the theta band contributes to selective attention, but that this mechanism is essentially unaffected by musical training.