Single-chain polymer nanoparticles (SCNPs) are soft nano-objects consisting of uni-macromolecular chains collapsed to a certain degree by intramolecular crosslinking. The similarities between the behaviour of SCNPs and that of intrinsically disordered proteins suggest that SCNPs in concentrated solutions can be used as models to design artificial micro-environments, which mimic many of the general aspects of cellular environments. In this work, the self-assembly into SCNPs of an amphiphilic random copolymer, composed by oligo(ethylene glycol)methyl ether methacrylate (OEGMA) and 2-acetoacetoxy ethyl methacrylate (AEMA), has been investigated by means of the dielectric relaxation of water. Direct evidence of segregation of the AEMA repeating units is provided by comparison with the dielectric relaxation of water in similar solutions of the linear hydrophilic polymer, P(OEGMA). Furthermore, the results of comparative studies with similar water solutions of an amphiphilic block copolymer forming multi-chain micelles support the single-chain character of the self-assembly of the random copolymer. The overall obtained results highlight the suitability of the dielectric spectroscopy to confirm the self-assembly of the amphiphilic random copolymers into globular like core-shell single-chain nanoparticles at a concentration well above the overlap concentration.