A coherent sheaf is a vector bundle over subvariety?

Over a complex manifold, can every coherent sheaf be seen as a holomorphic vector bundle over an analytic subset?

• I'm not sure what you mean by that either, but given a coherent sheaf $\mathcal E$ on a complex manifold $X$, there exists a non-empty Zariski open subset $U\subset X$ such that $\mathcal E|_U$ is locally free, hence is the sheaf of sections of a holomorphic vector bundle $E$ on $U$. – Henri Mar 13 at 17:38