Context. During the past decade, several studies reported a correlation between chemical abundances of stars and condensation temperature (also known as Tc trend). However, the real astrophysical nature of this correlation is still debated. Aims: The main goal of this work is to explore the possible dependence of the Tc trend on stellar Galactocentric distances, Rmean. Methods: We used high-quality spectra of about 40 stars observed with the HARPS and UVES spectrographs to derive precise stellar parameters, chemical abundances, and stellar ages. A differential line-by-line analysis was applied to achieve the highest possible precision in the chemical abundances. Results: We confirm previous results that [X/Fe] abundance ratios depend on stellar age and that for a given age, some elements also show a dependence on Rmean. When using the whole sample of stars, we observe a weak hint that the Tc trend depends on Rmean. The observed dependence is very complex and disappears when only stars with similar ages are considered. Conclusions: To conclude on the possible dependence of the Tc trend on the formation place of stars, a larger sample of stars with very similar atmospheric parameters and stellar ages observed at different Galactocentric distances is needed. Based on observations collected with the HARPS spectrograph at the 3.6-m telescope (program ID: 095.D-0717(A)), installed at the La Silla Observatory, ESO (Chile), with the UVES spectrograph at the 8-m Very Large Telescope (program ID: 095.D-0717(B)), installed at the Cerro Paranal Observatory, ESO (Chile). Also based on data obtained from the ESO Science Archive Facility under request numbers: vadibekyan180760, vadibekyan180762, vadibekyan180764, vadibekyan180768, vadibekyan180769, vadibekyan180771, vadibekyan180773, vadibekyan180778, and vadibekyan180779.Tables with stellar parameters and chemical abundances are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/592/A87