Solar surface convection displays highly localized sinks where cold plasma returns to the solar interior. On its way to being engulfed by a downdraft the plasma can also advect and intensify magnetic fields up to kG field strengths. Such theoretical predictions strengthen the idea that localized downdrafts are places where the concentration of magnetic fields is favored. The observational discovery of convectively driven sinks is rather recent, however, and its role in the formation and evolution of quiet-Sun magnetic features is still poorly characterized. In our work, we provide both quantitative and qualitative bases for the association between sinks and magnetic fields using high spatial resolution spectropolarimetric data acquired with the Imaging Magnetograph eXperiment on board Sunrise. We find 3.1 x 10-3 sinks Mm-2 minute-1 located at mesogranular vertices. These sinks are associated to (1) horizontal velocity flows converging to a central point and (2) long-lived downdrafts. The spatial distribution of magnetic fields in the quiet Sun is also examined. The strongest magnetic fields are preferentially located at sinks. We find that 40% of the pixels with longitudinal component of the magnetic field higher than 500 G are located in the close neighborhood of sinks. The study of individual examples reveal that sinks can play an important role in the evolution of quiet-Sun magnetic features.