We investigate in-gap states emerging when a single 3d transition metal impurity is embedded in topological insulators (Bi 2 Te 3 and Bi 2 Se 3 ). We use a combined approach relying on first-principles calculations and an Anderson impurity model. By computing the local density of states of Cr, Mn, Fe, and Co embedded not only in surfaces of Bi 2 Te 3 and of Bi 2 Se 3 but also in their bulk phases, we demonstrate that in-gap states originate from the hybridization of the electronic states of the impurity with bulk bands and not with the topological surface states as is usually assumed. This finding is analyzed using a simplified Anderson impurity model. These observations are in contradiction with the prevailing models used to investigate the magnetic doping of topological insulators [R. R. Biswas et al., Phys. Rev. B 81, 233405 (2010)], which attribute the origin of the in-gap states to the hybridization with the topological surface states.