The statement of the Novikov conjecture is a bit esoteric. Does the following simplified conjecture have any known counterexamples?
C: For a smooth closed 4n-fold $M$, the Pontryagin numbers are homotopy invariant. That is given $f: M \to N$ a homotopy equivalence with $N$ likewise closed and smooth 4n-fold, all Pontryagin numbers of $M,N$ coincide. As far as I can see this is not implied by the Novikov conjecture.