It seems that there is not much research concerning the anatomical localization of primitive reflexes. For instance, Schott & Rossor (2003) state in the conclusion of their review
The complexity of
many of these responses makes it perhaps unsurprising that
detailed anatomical localisation, despite the availability of
structural and functional imaging, has in general not been
However, at least for the grasp reflex, they discuss an involvement of frontal areas.
Schott, JM Rossor M (2003). The grasp and other primitive reflexes. J Neurol Neurosurg Psychiatry 74(5): 558–560. [DOI] [PDF]