Pyrometallurgical metal production results in side streams, such as dusts and slags, which are carriers of metals, though commonly containing lower metal concentrations compared to the main process stream. In order to improve the circular economy of metals, selective leaching of copper from an intermediate raw material originating from primary base metal production plant was investigated. The raw material investigated was rich in Cu (12.5%), Ni (2.6%), Zn (1.6%), and Fe (23.6%) with the particle size D80 of 124 µm. The main compounds present were nickel ferrite (NiFe2O4), fayalite (Fe2SiO4), cuprite (Cu2O), and metallic copper. Leaching was studied in 16 different solutions. The results revealed that copper phases could be dissolved with high yield (>90%) and selectivity towards nickel (Cu/Ni > 7) already at room temperature with the following solutions: 0.5 M HCl, 1.5 M HCl, 4 M NaOH, and 2 M HNO3. A concentration of 4 M NaOH provided a superior selectivity between Cu/Ni (340) and Cu/Zn (51). In addition, 1–2 M HNO3 and 0.5 M HCl solutions were shown to result in high Pb dissolution (>98%). Consequently, 0.5 M HCl leaching is suggested to provide a low temperature, low chemical consumption method for selective copper removal from the investigated side stream, resulting in PLS (pregnant leach solution) which is a rich in Cu and lead free residue, also rich in Ni and Fe.