  We investigate the parity nonconservation (PNC) effect in the dielectronic
recombination (DR) of a polarized electron with a heavy He-like ion into
doubly-excited $((1s 2p_{1/2})_{0} n{\kappa})_{1/2}$ and $\left(\left(1s
2s\right)_{0} n{\kappa}\right)_{1/2}$ states of Li-like ion. We determine the
nuclear charge number $Z$ for which these opposite-parity levels are near to
cross and, therefore, the PNC effect will be significantly enhanced.
Calculations are performed for quantum numbers $n \geq 4$ and $\kappa = \pm 1$.
