Is there a universal construction for Davies-Meyer hash functions?

My understanding is that there exists no strong pseudorandom permutation for which the Davies-Meyer construction is known to yield a provably collision-resistant hash function. Were I mean provably in the sense of invoking no assumptions like the ideal cipher model.

But my question is, does there exist a universal construction for the Davies-Meyer construction? That is, does there exist a strong pseudorandom permutation F such that if there exists at least one strong pseudorandom permutation whose Davies-Meyer construction is collision-resistant, then the Davies-Meyer construction based on F is collision-resistant?