The Cannon Conjecture for a torsionfree hyperbolic group G with boundary homeomorphic to S^2 says that G is the fundamental group of an aspherical closed 3-manifold M. It is known that then M is a hyperbolic 3-manifold. We prove the stable version that for any closed manifold N of dimension greater or equal to two there exists a closed manifold M together with a simple homotopy equivalence from M to N times BG. If N is aspherical and its fundamental group satisfies the Farrell-Jones Conjecture, then M is unique up to homeomorphism.