Milnor K-theory description of zero-cycles on quasi-projective schemes

Let $X$ be a quasi-projective scheme of dimension $d$ over an algebraically closed field $k$ of characteristic zero. Let $CH^d(X)$ denote the Chow group of zero-cycles and let $\mathcal K^M_d$ be the Zariski sheaf of Milnor $K$-groups. Milnor K-theory zero-cycle conjecture. There is an isomorphism

$$CH^d(X)\cong H^d_{Zar}(X,\mathcal K^M_d).$$

This is proposed as an expected extension of the smooth-scheme description to singular varieties; the supplied text says it is strongly suspected and does not report a proof or disproof.