Rhenium(I) tricarbonyl complexes have been described as suitable fluorophores, particularly for biological applications. fac-[Re(CO)3(N,N)L](0 or 1+) complexes, where N,N is a substituted dinitrogenated ligand (bipyridine or derivatives with relatively small substituents) and L the ancillary ligand [a pyridine Schiff base (PSB) harboring an intramolecular hydrogen bond (IHB)], have presented promissory results concerning their use as fluorophores, especially for walled cells (i.e., bacteria and fungi). In this work, we present a relativistic theoretical analysis of two series of fac-[Re(CO)3(N,N)PSB]1+ complexes to predict the role of the IHB in the ancillary ligand concerning their photophysical behavior. N,N corresponds to 2,2'-bipyridine (bpy) (series A) or 4,4'-bis(ethoxycarbonyl)-2,2'-bipyridine (deeb) (series B). We found that all the complexes present absorption in the visible light range. In addition, complexes presenting a PSB with an IHB exhibit luminescent emission suitable for biological purposes: large Stokes shift, emission in the range of 600-700 nm, and τ in the order of 10-2 to 10-3 s. By contrast, complexes with PSB lacking the IHB show a predicted emission with the lowest triplet excited-state energy entering the NIR region. These results suggest a role of the IHB as an important switcher between visible and NIR emissions in this kind of complexes. Since the PSB can be substituted to modulate the properties of the whole Re(I) complex, it will be interesting to explore whether other substitutions can also affect the photophysical properties, mainly the emission range.