The rare-earth elements (REEs) are considered as some of the most critical elements in the EU and the USA today. E-scrap, such as end-of-life neodymium magnets, could be a viable secondary source for the recovery of these elements. Neodymium magnets (NdFeB) consist of considerable amounts of Nd, Dy, Pr, and some other REEs, depending on the specific application. Apart from REEs, neodymium magnets are made up of around 60% iron, which can pose a challenge in their recycling. For example, iron can be dissolved along with other elements during leaching or co-extracted during solvent extraction. In this work, extraction of REEs with TODGA (tetraoctyl-diglycolamide) from a real leachate, obtained by neodymium magnet powder dissolution in nitric acid, was studied. The goal was to selectively extract the REEs from other elements in the solution. TODGA was used as the extracting agent due to its selective extraction properties for REEs and other f-block elements. The influence of the diluent on the overall extraction and the selectivity of the extraction was studied in order to determine application feasibility of future processes. To this end, experiments using Solvent 70 (hydrocarbons C11-C14, B0.5 wt% aromatics), hexane, toluene, cyclohexanone and 1-octanol as the diluents were performed. TODGA has shown good selectivity between REEs and other elements in solution under almost all conditions, reaching the highest distribution ratios of REEs in the aliphatic diluents, while the distribution ratios of other non-REEs reach a mere value of 0.1. An exception was cyclohexanone, which has the ability to extract small amounts of ions itself. The highest separation factors between Dy and the light REEs (Nd and Pr) were observed with a 0.01 M solution of TODGA in Solvent 70. REEs, as group, were extracted with 0.1 M solutions of TODGA in all diluents except for cyclohexanone, which led to extraction of Al and B at amounts greater than 10%. Stripping with over 98% efficiency was achieved using MQ water in one step.