A major challenge of CO2 injection into saline aquifers is the risk of formation clogging due to salt precipitation. Capillary-driven flow of brine can provide a continuous transport of dissolved salt toward the dry zone around the injection well where it ultimately precipitates due to evaporation. In this study, core flooding experiments were performed in homogeneous coarse-textured cores and in layered cores consisting of a coarse-textured layer overlying a fine-textured layer. CO2 was injected through a well in the upper part of the cores, and the bottom parts functioned as brine sources. Impairment in injectivity was found due to accumulation of precipitated salt caused by capillary-driven flow from the brine sources to the upper dryer region. Compared to flow domains without a brine source, we found that capillary-driven upward flow at first prevents complete clogging because the porous medium remains wet, but eventually leads to a more severe clogging of the entire domain. The results show that after sufficient dry-out, a coarse-textured injection layer can draw brine from an underlying fine-textured layer by capillary forces. A connected fine-textured layer can therefore contribute to salt precipitation and clogging of the injection layer.