Context. One of the most metal-rich open cluster of the Galaxy, NGC 6253 is a target of special interest in the search for extrasolar planets, the study of stellar populations, and the chemical/dynamical evolution of the Galactic disk. Aims. We present the results of two photometric campaigns and a VLT multi-epoch radial velocity survey toward the open cluster NGC 6253. We complement our analysis with photometric, proper motion, and radial velocity data available from previous studies of this cluster, and analyze three planetary candidates found in the field of NGC 6253. Methods. We derived homogeneous radial velocity measurements for stars located at the turn-off, sub-giant, red-giant branch, redclump, and blue straggler regions of the cluster. We also analyzed a comparison sample of surrounding field stars. Spectra were obtained with the UVES and GIRAFFE spectrographs at the VLT during three epochs in August 2008. Results. The three UVES measurements acquired for our brightest transiting candidate (V = 15.26) are all consistent within their errors (200 m/s), but were acquired at very similar orbital phases. The mean radial velocity of this object is not consistent with the cluster recession velocity, which rules out cluster membership except in the case of a binary system. This star is worth further analysis with high-precision spectroscopy. For our faintest candidate (V = 18.247), we were able to exclude the observed transits being caused by a close-by stellar companion, but more precise measurements will be needed to derive an orbital fit and to study other possible scenarios. For the remaining candidate, no measurements were acquired probably because of bad fiber positioning. The mean radial velocity of the cluster is (RV cl ± σ cl ) = (−29.11 ± 0.85) km s −1 . Using both radial velocities and proper motions, we identified 35 cluster members. Our results are in good agreement with past radial velocity and photometric measurements. Furthermore, using our photometry, astrometry, and spectroscopy we identified a new eclipsing binary system member of the cluster. Conclusions. We discussed the possibility of detecting substellar companions (brown dwarfs and planets) with the radial velocity technique (both with UVES/GIRAFFE and HARPS) around turn-off stars of old open cluster. We isolated 5 stars that are optimal targets for searching for planetary mass companions with HARPS. Our optimized strategy minimizes the observing time requested to isolate and followup on the best planetary candidates in cluster with high-precision spectrographs, an important aspect given the faint target stars.