Mahdavi-Hezavehi's weak Kurosh problem

Let $D$ be a non-commutative division ring algebraic over its center. A division subring is centrally finite if it has finite dimension over its center. Mahdavi-Hezavehi's weak Kurosh problem. Every non-commutative division ring algebraic over its center contains a centrally finite non-commutative division subring. The source presents this as a weak version of the Kurosh problem; the supplied text gives no resolution.