  We present a new embedding scheme for the locally self-consistent method to
study disordered electron systems. We test this method in a tight-binding basis
and apply it to the single band Anderson model. The local interaction zone is
used to efficiently compute the local Green's function of a supercell embeded
into a local typical medium. We find a quick convergence as the size of the
local interaction zone which reduces the computational costs as expected. This
method captures the Anderson localization transition and accurately predicts
the critical disorder strength. The present work opens the path towards the
development of a typical medium embedding scheme for the $O(N)$ multiple
scattering methods.
