# Reference request: Existence of plurisubharmonic potential for positive (1,1)-current on Stein (affine) manifold

I am looking for a reference for the following fact, which I believe should be true.

Let $X$ be a Stein manifold (or smooth affine variety over $\mathbb{C}$). If $\omega$ is a positive closed $(1,1)$-current over $X,$ then there exists a plurisubharmonic function $\varphi$ such that $\omega=i\partial\overline{\partial} \varphi.$ In practice, I am interested in cases when $X= \mathbb{C}^n$ and $X= (\mathbb{C}\setminus \{0\})^n$.

I found the local version of this statement in Demailly's Complex Analytic and Differential Geometry, Chapter III, Proposition 1.19.