existance of gradient conformal vector field on riemannian manifolds

Question

Let ‎$ ‎(M,g)‎ $ ‎be a Riemannian manifold. A gradient conformal vector field on ‎$ ‎M‎ $‎ is a conformal vector field ‎$ ‎X‎ $‎ which is at the same time the gradient of a function on ‎‎$ ‎M‎ $ ‎:‎ \begin{equation}‎ ‎X=‎\nabla f‎ ,‎ ‎L‎_{X}‎g=2‎\rho ‎g‎ \end{equation}‎‎ where $L‎$ is the Lie derivative. Is there always gradient conformal vector field on $M$? Thanks. ‎‎‎‎