The following theorem is due to Freyd.

Let $C$ be a category of pointed topological spaces including all finite-dimensional CW-complexes. Let $H:Cto mathrm{Set}$ be a homotopy invariant functor. There exists $f:Xto Y$ such that $f$ is not null-homotopic but $H(f)=H(star)$ where $star$ is null-homotopic.

Is there an analogue of this theorem in motivic homotopy theory?