SN 1572 (Tycho Brahe’s supernova) clearly belongs to the Ia (thermonuclear) type. It was produced by the explosion of a white dwarf (WD) in a binary system. Its remnant has been the first of this type to be explored in search of a possible surviving companion, the mass donor that brought the WD to the point of explosion. A high peculiar motion with respect to the stars at the same location in the Galaxy, mainly due to the orbital velocity at the time of the explosion, is a basic criterion for the detection of such companions. Radial velocities from the spectra of the stars close to the geometrical center of Tycho’s supernova remnant, plus proper motions of the same stars, obtained by astrometry with the Hubble Space Telescope (HST), have been used so far. In addition, a detailed chemical analysis of the atmospheres of a sample of candidate stars had been made. However, the distances to the stars remained uncertain. Now, the Second Gaia Data Release (DR2) provides unprecedented accurate distances, and new proper motions for the stars can be compared with those obtained from the HST. We consider the Galactic orbits that the candidate stars to the SN companion would have in the future. We do this to explore any kinematic peculiarity. We also locate a representative sample of candidate stars in the Toomre diagram. Using the new data, we re-evaluate the status of the candidates suggested thus far, as well as the larger sample of the stars seen in the central region of the remnant.