While theory and simulations indicate that galaxy mergers play an important role in the cosmological evolution of accreting black holes and their host galaxies, samples of Active Galactic Nuclei (AGN) in galaxies at close separations are still small. In order to increase the sample of AGN pairs, we undertook an archival project to investigate the X-ray properties of a SDSS-selected sample of 32 galaxy pairs with separations $le$150 kpc containing one optically-identified AGN, that were serendipitously observed by XMM-Newton. We discovered only one X-ray counterpart among the optically classified non-active galaxies, with a weak X-ray luminosity ($simeq$5$times$10$^{41}$ erg s$^{-1}$). 59% (19 out of 32) of the AGN in our galaxy pair sample exhibit an X-ray counterpart, covering a wide range in absorption corrected X-ray luminosity (5$times$10$^{41}$-2$times$10$^{44}$ erg s$^{-1}$). More than 79% of these AGN are obscured (column density $N_H>$10$^{22}$ cm$^{-2}$), with more than half thereof ({it i.e.}, about 47% of the total AGN sample) being Compton-thick. AGN/no-AGN pairs are therefore more frequently X-ray obscured (by a factor $simeq$1.5) than isolated AGN. When compared to a luminosity and redshift-matched sample of {it bona fide} dual AGN, AGN/no-AGN pairs exhibit one order-of-magnitude lower X-ray column density in the same separation range ($>$10 kpc). A small sample (4 objects) of AGN/no-AGN pairs with sub-pc separation are all heavily obscured, driving a formal anti-correlation between the X-ray column density and the galaxy pair separation in these systems. These findings suggest that the galactic environment has a key influence on the triggering of nuclear activity in merging galaxies.
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