We study the relation between mesogranular flows, convectively driven sinks and magnetic fields using high spatial resolution spectropolarimetric data acquired with the Imaging Magnetograph eXperiment on board Sunrise. We obtain the horizontal velocity flow fields of two quiet-Sun regions (31.2 × 31.2 Mm2) via local correlation tracking. Mesogranular lanes and the central position of sinks are identified using Lagrange tracers. We find 6.7× {10}-2 sinks per Mm2 in the two observed regions. The sinks are located at the mesogranular vertices and turn out to be associated with (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 components of the magnetic field stronger than 500 G are located in the close neighborhood of sinks. In contrast, the small-scale magnetic loops detected by Martínez González et al. in the same two observed areas do not show any preferential distribution at mesogranular scales. The study of individual examples reveals that sinks can play an important role in the evolution of quiet-Sun magnetic features.