The purpose of this study was to investigate whether Human Serum Albumin (HSA) can bind native human insulin and its A13–A19 and B12–B17 fragments, which are responsible for the aggregation of the whole hormone. To label the hormone and both hot spots, so that their binding positions within the HSA could be identified, 4-(1-pyrenyl)butyric acid was used as a fluorophore. Triazine coupling reagent was used to attach the 4-(1-pyrenyl)butyric acid to the N-terminus of the peptides. When attached to the peptides, the fluorophore showed extended fluorescence lifetimes in the excited state in the presence of HSA, compared to the samples in buffer solution. We also analyzed the interactions of unlabeled native insulin and its hot spots with HSA, using circular dichroism (CD), the microscale thermophoresis technique (MST), and three independent methods recommended for aggregating peptides. The CD spectra indicated increased amounts of the α-helical secondary structure in all analyzed samples after incubation. Moreover, for each of the two unlabeled hot spots, it was possible to determine the dissociation constant in the presence of HSA, as 14.4 µM (A13–A19) and 246 nM (B12–B17). Congo Red, Thioflavin T, and microscopy assays revealed significant differences between typical amyloids formed by the native hormone or its hot-spots and the secondary structures formed by the complexes of HSA with insulin and A13–A19 and B12–B17 fragments. All results show that the tested peptide-probe conjugates and their unlabeled analogues interact with HSA, which inhibits their aggregation.