  The rare $B_c \to D_{s,d}^{*} l^+ l^-$ decays are investigated in the
framework of the three point QCD sum rules approach. Considering the gluon
condensate corrections to the correlation function, the form factors relevant
to these transitions are calculated. The total decay width and branching ratio
for these decays are also evaluated. The results for the branching ratios are
in good agreement with the quark models.
