The free group algebra conjecture for division rings

Let $D$ be a division ring with center $k$. Let a free group algebra over $k$ mean the group algebra over $k$ of a free group embedded in $D$. Free group algebra conjecture. If $D$ is finitely generated and infinite dimensional over $k$, then $D$ contains a free group algebra over $k$. This is presented as a generalization of the preceding free-subalgebra and free-group conjectures; the source gives no resolution status.