Among potential sources of scandium and other rare earth elements (REEs) there are semiproducts generated by the alumina industry. They include red mud and ESP dust generated by sintering plants. Most of the previous research studies focused on red mud leaching using a variety of strong acids. However, because of the need to neutralize the caustic alkali present in red mud, as well as to dissolve iron and other macrocomponents, the above process is associated with a high consumption of reagents. This paper examines the possibility to selectively recover REEs from ESP dust at high pH values in the presence of magnesium cations. It is shown that the prior water leaching of ESP dust helps achieve a double rise in the REE concentration and considerably lower the concentration of Na2O in the solid residue. For selective recovery of REEs, the authors used weak solutions (pH = 2÷5) of sulphuric acid with magnesium sulphate. The latter help to desorb REEs from the surface of minerals contained in the solid residue. Over 75% Sc was recovered through solid residue leaching conducted at the temperature of 80 oC, liquid-to-solid ratio of 10:1 and duration of 60 min at pH = 2. The recovery of iron and titanium did not exceed 1–5%. With all other conditions being equal, raising pH to 3.5 would lead to a drop in the scandium recovery to 63% while the recovery of iron and titanium would drop to 0.2%. It was also found that, as the result of sulphuric acid leaching, the calcium that is present in the initial ESP dust gets precipitated in the form of gypsum and a certain amount of REEs may get carried away. This research was carried out as part of Grant No. 22-29-01515 of the Russian Science Foundation; the concentration of rare earth elements in the solid residue was determined through inductively coupled plasma mass spectrometry, supported through an assignment of the Government of the Russian Federation under Grant No. 075-03-2021-051/5.