  We compared high-contrast near-infrared images of the core of R136 taken by
VLT/SPHERE, in two epochs separated by 3.06 years. For the first time we
monitored the dynamics of the detected sources in the core of R136 from a
ground-based telescope with adaptive optics. The aim of these observations was
to search for High prOper Motion cAndidates (HOMAs) in the central region of
R136 (r<6") where it has been challenging for other instruments. Two bright
sources (K<15mag and V<16mag) are located near R136a1 and R136c (massive WR
stars) and have been identified as potential HOMAs. These sources have
significantly shifted in the images with respect to the mean shift of all
reliable detected sources and their neighbours, and six times their own
astrometric errors. We calculate their proper motions to be 1.36\pm0.22 mas/yr
(321\pm52 km/s) and 1.15\pm0.11 mas/yr (273\pm26 km/s). We discuss different
possible scenarios to explain the magnitude of such extreme proper motions, and
argue for the necessity to conduct future observations to conclude on the
nature of HOMAs in the core of R136.
