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The systematic alignment of low-frequency brain oscillations with the acoustic speech envelope signal is well established and has been proposed to be crucial for actively perceiving speech. Previous studies investigating speech-brain coupling in source space are restricted to univariate pairwise approaches between brain and speech signals, and therefore speech tracking information in frequency-specific communication channels might be lacking. To address this, we propose a novel multivariate framework for estimating speech-brain coupling where neural variability from source-derived activity is taken into account along with the rate of envelope's amplitude change (derivative). We applied it in magnetoencephalographic (MEG) recordings while human participants (male and female) listened to one hour of continuous naturalistic speech, showing that a multivariate approach outperforms the corresponding univariate method in low- and high frequencies across frontal, motor, and temporal areas. Systematic comparisons revealed that the gain in low frequencies (0.6 - 0.8 Hz) was related to the envelope's rate of change whereas in higher frequencies (from 0.8 to 10 Hz) it was mostly related to the increased neural variability from source-derived cortical areas. Furthermore, following a non-negative matrix factorization approach we found distinct speech-brain components across time and cortical space related to speech processing. We confirm that speech envelope tracking operates mainly in two timescales (δ and θ frequency bands) and we extend those findings showing shorter coupling delays in auditory-related components and longer delays in higher-association frontal and motor components, indicating temporal differences of speech tracking and providing implications for hierarchical stimulus-driven speech processing.