Nef cotangent conjecture for projective manifolds with Stein universal cover

Let $Y$ be a projective manifold, and let $\widetilde{Y}$ be its universal cover. Nef cotangent conjecture. If $\widetilde{Y}$ is a Stein manifold, then the cotangent bundle $\Omega_Y^1$ is nef. The source notes a weaker result when the universal cover is a bounded domain in a Stein manifold, while the stated conjecture remains open.