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In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital) entanglement entropies (von Neumann and linear) can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization) for such a doubly excited state, is also calculated.