Yeast self-perpetuating protein aggregates (yeast prions) provide a framework to investigate the interaction of misfolded proteins with the protein quality control machinery. The major component of this system that facilitates propagation of all known yeast amyloid prions is the Hsp104 chaperone that catalyzes fibril fragmentation. Overproduction of Hsp104 cures some yeast prions via a fragmentation-independent mechanism. Importantly, major cytosolic chaperones of the Hsp40 group, Sis1 and Ydj1, oppositely affect yeast prion propagation, and are capable of stimulating different activities of Hsp104. In this work, we developed a quantitative method to investigate the Hsp40 binding to amyloid aggregates. We demonstrate that Sis1 binds fibrils formed by the Sup35NM protein with higher affinity compared to Ydj1. Moreover, the interaction of Sis1 with the fibrils formed by the other yeast prion protein, Rnq1, is orders of magnitude weaker. We show that the deletion of the dimerization domain of Sis1 (crucial for the curing of [PSI+] by excess Hsp104) decreases its affinity to both Sup35NM and Rnq1 fibrils. Taken together, these results suggest that tight binding of Hsp40 to the amyloid fibrils is likely to enhance aggregate malpartition instead of fibril fragmentation.