von Neumann algebraic von Neumann problem

A II$_1$ factor is nonamenable if it is not amenable, and $L(\mathbb F_2)$ denotes the group II$_1$ factor of the free group on two generators. von Neumann algebraic von Neumann problem. Every nonamenable II$_1$ factor contains a copy of $L(\mathbb F_2)$. This is described as a well-known conjecture, and the source gives no evidence of a resolution.