Rising sound intensity often signals an approaching sound source and can serve as a powerful warning cue, eliciting phasic attention, perception biases and emotional responses. How the evaluation of approaching sounds unfolds over time remains elusive. Here, we capitalised on the temporal resolution of magnetoencephalograpy (MEG) to investigate in humans a dynamic encoding of perceiving approaching and receding sounds. We compared magnetic responses to intensity envelopes of complex sounds to those of white noise sounds, in which intensity change is not perceived as approaching. Sustained magnetic fields over temporal sensors tracked intensity change in complex sounds in an approximately linear fashion, an effect not seen for intensity change in white noise sounds, or for overall intensity. Hence, these fields are likely to track approach/recession, but not the apparent (instantaneous) distance of the sound source, or its intensity as such. As a likely source of this activity, the bilateral inferior temporal gyrus and right temporo-parietal junction emerged. Our results indicate that discrete temporal cortical areas parametrically encode behavioural significance in moving sound sources where the signal unfolded in a manner reminiscent of evidence accumulation. This may help an understanding of how acoustic percepts are evaluated as behaviourally relevant, where our results highlight a crucial role of cortical areas.