Jordan-domain conjecture for bounded immediate basins of transcendental entire functions

Let $f$ be a transcendental entire function, and let $D$ be an immediate attracting or parabolic basin. If $D$ is bounded, then $D$ is a Jordan domain.

Jordan-domain conjecture. Every bounded immediate attracting or parabolic basin of a transcendental entire function is a Jordan domain.

This is motivated by the result that all bounded attracting and parabolic Fatou components of polynomials are Jordan domains. The statement is proposed for the transcendental entire setting without additional dynamical assumptions on $f$.