Copper(II) complexes have become a potential alternative to the use of platinum drugs in cancer therapy due to their multi-target mode of action. In this context, we report the syntheses of new mononuclear and dinuclear coordination compounds of this element, 1 and 2, derived from the ligand 5-methylsalicylaldehyde 2-furoyl hydrazone (H2L). All three compounds were structurally and spectroscopically characterized, both in the solid state and in solution. In 1, Cu is coordinated by three donor-atoms from the hydrazonic ligand and one chloride ion. H2L is deprotonated at the phenol oxygen. The dinuclear complex 2 is, on the other hand, a dimeric form of 1 in which the chloride ions of a pair of mononuclear units are lost and phenoxo bridges take their places, double-connecting the metal centres and resulting in a single species with the ligand fully deprotonated. The compounds were fairly stable in aqueous medium at room temperature. An experimental-theoretical combined approach demonstrated that all of them are able to bind human serum albumin (HSA), although at different sites and with diverse stoichiometries and affinities (as concluded by the calculated binding energies). In view of this, and due to the well-known antiproliferative activity of hydrazone-containing copper complexes, we consider the compounds presented in here promising, and believe that they deserve more profound studies regarding the assessment of their potential against tumour cell lines.