Conformal polynomial model conjecture for holomorphic functions on the disk

Let $f$ be holomorphic on a neighborhood of the closure of the unit disk $\mathbb{D}$. An injective holomorphic function is a holomorphic map that is one-to-one. Conformal polynomial model conjecture. There is an injective holomorphic function $\phi: \mathbb{D} \to \mathbb{C}$ and a polynomial $p$ such that

$$f=p \circ \phi$$

on $\mathbb{D}$. This conjecture concerns representing holomorphic functions on the disk, after an injective holomorphic change of variables, as polynomial maps; the supplied material does not state whether it is open, resolved, or disproved.