  Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a
projective manifold $X$, any singular positive metric on the line bundle
$L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular
positive metric on $L$. In this paper, we prove that the extendability of
singular positive metrics on a line bundle along a subvariety implies the
ampleness of the line bundle.
