Normal holonomy conjecture for nonnegatively curved connection metrics

Let $M^n$ be a manifold, and consider a connection metric of nonnegative curvature on an $\mathbb{R}^k$-bundle over $M^n$. The normal holonomy group is the holonomy group of the normal connection of the soul.

Normal holonomy conjecture. The normal holonomy group is isomorphic to a subgroup of $\operatorname{SO}(n)$.

This would generalize the preceding result for nonnegatively curved connection metrics on $\mathbb{R}^3$-bundles over $S^2$, where the normal holonomy group is trivial or isomorphic to $S^1$. The statement is presented as a natural generalization; no resolution is given here.