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Bob Thomason proved that there is no Milnor K-theory functor for schemes, with a reasonable map to Quillen K-theory, in:

Le principe de scindage et l'inexistence d'une $K$-theorie de Milnor globale. (French) [The splitting principle and the nonexistence of a global Milnor $K$-theory] Topology 31 (1992), no. 3, 571--588.

• John
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Bob Thomason proved that there is no Milnor K-theory functor for schemes with a reasonable map to Quillen K-theory, in:

Le principe de scindage et l'inexistence d'une $K$-theorie de Milnor globale. (French) [The splitting principle and the nonexistence of a global Milnor $K$-theory] Topology 31 (1992), no. 3, 571--588.

• John