  We show that a singular Hermitian metric on a holomorphic vector bundle over
a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can
be approximated by a sequence of smooth Hermitian metrics with the same
curvature negativity. We also show that a smooth Hermitian metric on a
holomorphic vector bundle over a Stein manifold restricted to a submanifold
which is negative in the sense of Griffiths (resp. Nakano) can be extended to
the whole bundle with the same curvature negativity.
