We show here the existence of the indirect coupling of electron and magnetic or nuclear ion spins in self-assembled quantum dots mediated by electron-electron interactions. With a single localized spin placed in the center of the dot, only the spins of electrons occupying the zero angular momentum states couple directly to the localized spin. We show that when the electron-electron interactions are included, the electrons occupying finite angular momentum orbitals interact with the localized spin. This effective interaction is obtained using exact diagonalization of the microscopic Hamiltonian as a function of the number of electronic shells, shell spacing, and anisotropy of the electron-Mn exchange interaction. The effective interaction can be engineered to be either ferromagnetic or antiferromagnetic by tuning the parameters of the quantum dot.