  Given a complex simple Lie algebra $\mathfrak{g}$ and a positive integer
$\ell$, under the assumption $\lambda\gg\mu$, we show that irreducible
representations of $\mathfrak{g}$ of the form $V(\lambda +w\mu)$, $w\in W,$
with level at most $\ell$ appear in the fusion product of $V(\lambda)$ and
$V(\mu)$. This verifies the existence of PRV components for the fusion product
in this special case.
