We investigate the low-lying octupole response of neutron-rich Ni isotopes beyond the N = 50 shell closure using the Skyrme-Hartree-Fock-Bogoliubov mean fields and the continuum quasi-particle random phase approximation. Performing detailed numerical analyses employing the Skyrme parameter set SLy4 and a density-dependent delta interaction of the mixed type, we show that a neutron mode emerges above the neutron separation energy as a consequence of the weak binding of neutrons and that it strongly influences the di-neutron correlation.