Makar-Limanov's descent conjecture for free associative subalgebras

Let $K$ be a field, let $A$ be an associative $K$-algebra, and let $F$ be a field extension of $K$.

Makar-Limanov's conjecture. If $F\otimes_K A$ contains a free $K$-algebra on at least two free generators, then $A$ also contains a free $K$-algebra on the same number of free generators.

This conjecture asks whether the existence of a free associative subalgebra descends along field extensions. The source attributes it to L. Makar-Limanov; its resolution is not specified here.