The embedding conjecture for simple A1-invariant sheaves

Let $k$ be the base field, and let ${\mathcal F}$ be a simple ${\mathbb A}^1$-invariant sheaf. Write $\Omega^{\bullet}_{k(Y)|k}$ for the graded differential forms of the function field $k(Y)$ over $k$. Embedding conjecture. Any simple ${\mathbb A}^1$-invariant sheaf can be embedded into the sheaf $Y\mapsto\Omega^{\bullet}_{k(Y)|k}$. This is presented as one of the principal problems concerning ${\mathbb A}^1$-invariant sheaves; the source gives no resolution.