Cobalt (Co) is an essential metal for sustainable technologies, including electric vehicles and energy storage systems. Its selective recovery from complex leachates remains a challenge due to the co-presence of nickel (Ni) and manganese (Mn). This work examines the influence of the extracting phase composition on the solvent extraction (SX) of Co from highly acidic chloride media (pH ≈ 0.86, 6–12 M LiCl) containing Ni and Mn. Trioctylphosphine oxide (TOPO) was used as the extractant, dissolved in three different media: dodecane, the ionic liquid (IL) 1-methyl-3-octylimidazolium bis(trifluoromethylsulfonyl)imide ([C₈mim][Tf₂N]), and the hydrophobic eutectic solvent (HES) TOPO:decanoic acid (1:1). The extraction of Co increased with LiCl concentration, consistent with the formation of anionic Co–chloride complexes, while Ni extraction remained negligible due to its high hydration energy. Slope analysis confirmed a 2:1 TOPO:Co stoichiometry for all systems, indicating a solvation-controlled extraction mechanism. Both the IL and the HES improved Co recovery compared with the molecular diluent, achieving high selectivity with minimal Mn co-extraction. Volatility tests showed severe solvent loss for dodecane, whereas [C₈mim][Tf₂N] and TOPO:decanoic acid exhibited excellent thermal stability (<2% mass loss) and low water uptake (<2%). These results highlight the potential of IL and HES as sustainable alternatives to conventional organic diluents. Among the systems studied, TOPO:decanoic acid (1:1) displayed the best balance of extraction efficiency, selectivity, and stability, representing a promising medium for Co recovery from chloride solutions.