Li-Zheng's Hopf-type conjecture for Kähler manifolds

Let $M$ be an $n$-dimensional Kähler manifold with non-positive holomorphic bisectional curvature, and suppose that its Ricci curvature is quasi-negative. Li-Zheng's conjecture. The signed Euler characteristic satisfies

$$(-1)^n\chi(M)>0.$$

This is proposed as a complex analogue of the classical Hopf conjecture. The supplied text gives no evidence that it has been resolved.