Improvements in cancer diagnostics and therapy have recently attracted the interest of many different branches of science. This study presents one of the new possible approaches in the diagnostics and therapy of cancer by using polymeric chelates as carriers. Graft copolymers with a backbone containing 8-hydroxyquinoline-5-sulfonic acid chelating groups and poly(ethylene oxide) hydrophilic grafts are synthesized and characterized. The polymers assemble and form particles after the addition of a biometal cation, such as iron or copper. The obtained nanoparticles exhibit a hydrodynamic diameter of around 25 nm and a stability of at least several hours, which are counted as essential parameters for biomedical purposes. To prove their biodegradability, a model degradation with deferoxamine is performed and, together with high radiolabeling efficiency with copper-64, their possible use for nuclear medicine purposes is demonstrated.