  We consider a holomorphic foliation $\mathcal{F}$ of codimension $k\geq 1$ on
a homogeneous compact K\"ahler manifold $X$ of dimension $n>k$. Assuming that
the singular set $Sing(\mathcal{F})$ of $\mathcal{F}$ is contained in an
absolutely $k$-convex domain $U\subset X$, we prove that the determinant of
normal bundle $\det(N_{\mathcal{F}})$ of $\mathcal{F}$ cannot be an ample line
bundle, provided $[n/k]\geq 2k+3$. Here $[n/k]$ denotes the largest integer
$\leq n/k.$
