  The formation of spherical polaron clusters is studied within the
Fr$\ddot{o}$hlich polaron theory. In a dilute polaron gas, using the non-local
statistical approach and the polaron pair interaction obtained within the Pekar
strong coupling theory, the homogeneous phase results to be unstable toward the
appearance of polaron clusters. The physical conditions of formation for the
clusters are determined calculating the critical values of electron-phonon
interaction for which bound states in the collective polaron potential develop.
Finally the sequence in the filling of the states is found and the stability of
the clusters is assessed.
