In the local Universe there exists a rare population of compact galaxies resembling the high-redshift quiescent population in mass and size. It has been found that some of these objects have survived largely unchanged since their formation at high-z. They are called relic galaxies. With the goal of finding relic galaxies, we searched the SDSS-MaNGA DR15 release for massive compact galaxies. We find that massive compact galaxies are mostly composed of old, metal-rich and alpha enhanced stellar populations. In terms of kinematics, massive compact galaxies show ordered rotation in their velocity fields and σ* profiles rising towards the center. They are predominantly fast rotators and show increased rotational support when compared to a mass-matched control sample of average-sized early-type galaxies. These properties are consistent with these objects being relic galaxies. However, to confirm their relic status, we need to probe larger radii (⪎3Re) than probed with the current data.