Sufficient condition for $\langle Ax, Ay\rangle\leq \lambda^2_{max}\langle x, y\rangle$

Question

Question. Is there a ''non-trivial'' sufficient condition on $x, y\in \mathbb R^n$ such that $$\langle Ax, Ay\rangle\leq \lambda^2_{\max}\langle x, y\rangle$$ where $A\in \mathbb R^{m\times n}$ and $\lambda_{\max}>0$ is the largest singular value of $A$.

''Trivial'' case. If $x=y$, it is well-known that $$||Ax||^2\leq \lambda_{\max}^2||x||^2$$ and $\lambda_{\max}$ is called the spectral norm of $A$.