Small and elongated, cool and dense blob-like structures are being reported with high resolution telescopes in physically different regions throughout the solar atmosphere. Their detection and the understanding of their formation, morphology, and thermodynamical characteristics can provide important information on their hosting environment, especially concerning the magnetic field, whose understanding constitutes a major problem in solar physics. An example of such blobs is coronal rain, a phenomenon of thermal non-equilibrium observed in active region loops, which consists of cool and dense chromospheric blobs falling along loop-like paths from coronal heights. So far, only off-limb coronal rain has been observed, and few reports on the phenomenon exist. In the present work, several data sets of on-disk Hα observations with the CRisp Imaging SpectroPolarimeter (CRISP) at the Swedish 1-m Solar Telescope (SST) are analyzed. A special family of on-disk blobs is selected for each data set, and a statistical analysis is carried out on their dynamics, morphology, and temperature. All characteristics present distributions which are very similar to reported coronal rain statistics. We discuss possible interpretations considering other similar blob-like structures reported so far and show that a coronal rain interpretation is the most likely one. The chromospheric nature of the blobs and the projection effects (which eliminate all direct possibilities of height estimation) on one side, and their small sizes, fast dynamics, and especially their faint character (offering low contrast with the background intensity) on the other side, are found as the main causes for the absence until now of the detection of this on-disk coronal rain counterpart.