Context. Transition disks offer the extraordinary opportunity to look for newly born planets and to investigate the early stages of planet formation. Aim. In this context we observed the Herbig A5 star MWC 758 with the L′-band vector vortex coronagraph installed in the near-infrared camera and spectrograph NIRC2 at the Keck II telescope, with the aim of unveiling the nature of the spiral structure by constraining the presence of planetary companions in the system. Methods. Our high-contrast imaging observations show a bright (ΔL′ = 7.0 ± 0.3 mag) point-like emission south of MWC 758 at a deprojected separation of ~20 au (r = 0.′′111 ± 0.′′004) from the central star. We also recover the two spiral arms (southeast and northwest), alre...