Cortical gyrification takes place predominantly during the second to third trimester, alongside other fundamental developmental processes, such as the development of white matter connections, lamination of the cortex and formation of neural circuits. The mechanistic biology that drives the formation cortical folding patterns remains an open question in neuroscience. In our previous work, we modelled the in utero diffusion signal to quantify the maturation of microstructure in transient fetal compartments, identifying patterns of change in diffusion metrics that reflect critical neurobiological transitions occurring in the second to third trimester. In this work, we apply the same modelling approach to explore whether microstructural maturation of these compartments is correlated with the process of gyrification. We quantify the relationship between sulcal depth and tissue anisotropy within the cortical plate (CP) and underlying subplate (SP), key transient fetal compartments often implicated in mechanistic hypotheses about the onset of gyrification. Using in utero high angular resolution multi-shell diffusion-weighted imaging (HARDI) from the Developing Human Connectome Project (dHCP), our analysis reveals that the anisotropic, tissue component of the diffusion signal in the SP and CP decreases immediately prior to the formation of sulcal pits in the fetal brain. By back-projecting a map of folded brain regions onto the unfolded brain, we find evidence for cytoarchitectural differences between gyral and sulcal areas in the late second trimester, suggesting that regional variation in the microstructure of transient fetal compartments precedes, and thus may have a mechanistic function, in the onset of cortical folding in the developing human brain.