The spatio-temporal distribution (4D) of water in porous materials plays a fundamental role in many natural and technological processes. The dynamics of water transport is strongly entangled with the material’s pore-scale structure. Understanding their correlation requires imaging simultaneously the 4D water distribution and the porous microstructure. To date, 4D images with high temporal and spatial resolution have been mainly acquired by attenuation-based X-ray micro-tomography, whereby pure water is substituted by saline solutions with high atomic number components to improve image contrast. The use of saline solutions is however not always desirable, as the altered fluid properties may affect the transport process as well or, as it is the case for hydrating cement-based materials, they may modify the chemical reactions and their kinetics. In this study, we aimed at visualizing pure water transport in porous building materials by a new implementation of fast Talbot interferometry-based multi-contrast X-ray micro-tomography at the P07 beamline of the Helmholtz-Zentrum Geesthacht at DESY. We report results from a mortar specimen imaged at three different stages during evaporative drying. We show the possibility of visualizing simultaneously the microstructure and the pore-scale water redistribution by the phase contrast images. In addition, different solid material phases are clearly distinguished in these images. The higher contrast between water and the porous substrate, achievable in the phase contrast images, compared with the attenuation ones, empowers new analysis and allows investigating the correlation between the drying process and the porous microstructure. The approach offers the possibility of studying other chemically inert or reactive water transport processes without any chemical or physical perturbation of the processes themselves.