Extremely preterm infants' hemodynamic instability places them at high risk of brain injury. Currently there is no reliable bedside method to continuously monitor cerebral hemodynamics in the neonatal intensive care unit (NICU). This paper reports a feasibility study to adapt and test an innovative speckle contrast diffuse correlation tomography (scDCT) device for noncontact, high-density, 3D imaging of cerebral blood flow (CBF) in preterm infants. The scDCT scans a focused point near-infrared illumination to multiple source positions for deep tissue penetration, and controls an electron multiplying charge-coupled-device camera with thousands of pixels to achieve a high-density sampling. The optimized scDCT for use in preterm infants was first evaluated against an established diffuse correlation spectroscopy in an infant-head-simulating phantom with known properties. The observed significant correlation between the two measurements verified the capability of scDCT for transcranial brain imaging. The insignificant influence of transparent incubator wall on scDCT measurements was then confirmed by comparing adult forearm blood flow responses to artery cuff occlusions measured inside and outside the incubator. Finally, the scDCT device was moved to the NICU to image CBF variations in two preterm infants. Infant #1 with no major organ deficits showed little CBF fluctuation over the first 3 weeks of life. Infant #2 showed a significant CBF increase after the 2 h pharmacotherapy for patent ductus arteriosus closure. While these CBF variations meet physiological expectations, the fact that no significant changes are noted with peripheral monitoring of blood oxygen saturation suggests necessity of direct cerebral monitoring. This feasibility study with timely technology development is an important and necessary step towards larger clinical studies with more subjects to further validate it for continuous monitoring and instant management of cerebral pathologies and interventions in the NICU.