The envelope of a speech signal is tracked by neural activity in the cerebral cortex. The cortical tracking occurs mainly in two frequency bands, theta (4–8 Hz) and delta (1–4 Hz). Tracking in the faster theta band has been mostly associated with lower-level acoustic processing, such as the parsing of syllables, whereas the slower tracking in the delta band relates to higher-level linguistic information of words and word sequences. However, much regarding the more specific association between cortical tracking and acoustic as well as linguistic processing remains to be uncovered. Here, we recorded EEG responses to both meaningful sentences and random word lists in different levels of signal-to-noise ratios (SNRs) that lead to different levels of speech comprehension as well as listening effort. We then related the neural signals to the acoustic stimuli by computing the phase-locking value (PLV) between the EEG recordings and the speech envelope. We found that the PLV in the delta band increases with increasing SNR for sentences but not for the random word lists, showing that the PLV in this frequency band reflects linguistic information. When attempting to disentangle the effects of SNR, speech comprehension, and listening effort, we observed a trend that the PLV in the delta band might reflect listening effort rather than the other two variables, although the effect was not statistically significant. In summary, our study shows that the PLV in the delta band reflects linguistic information and might be related to listening effort.