The dinuclear copper complex bearing a 2,7-disubstituted-1,8-naphthalenediol ligand, [(HtomMe){Cu(OAc)}2](OAc), a potential anticancer drug able to bind to two neighboring phosphates in the DNA backbone, is endowed with stronger cytotoxic effects and inhibition ability of DNA synthesis in human cancer cells as compared to cisplatin. In this study, the intrinsic binding ability of the charged complex [(HtomMe){Cu(OAc)}2]+ is investigated with representative phosphate diester ligands with growing chemical complexity, ranging from simple inorganic phosphate up to mononucleotides. An integrated method based on high-resolution mass spectrometry (MS), tandem MS, and infrared multiple photon dissociation (IRMPD) spectroscopy in the 600-1800 cm-1 spectral range, backed by quantum chemical calculations, has been used to characterize complexes formed in solution and delivered as bare species by electrospray ionization. The structural features revealed by IRMPD spectroscopy have been interpreted by comparison with linear IR spectra of the lowest-energy structures, revealing diagnostic signatures of binding modes of the dinuclear copper(II) complex with phosphate groups, whereas the possible competitive interaction with the nucleobase is silenced in the gas phase. This result points to the prevailing interaction of [(HtomMe){Cu(OAc)}2]+ with phosphate diesters and mononucleotides as a conceivable contribution to the observed anticancer activity.