  In this paper, we introduce and study the class $S$-$\mathcal{F}$-ML of
$S$-Mittag-Leffler modules with respect to all flat modules. We show that a
ring $R$ is $S$-coherent if and only if $S$-$\mathcal{F}$-ML is closed under
submodules. As an application, we obtain the $S$-version of Chase Theorem: a
ring $R$ is $S$-coherent if and only if any direct product of $R$ is $S$-flat
if and only if any direct product of flat $R$-modules is $S$-flat.
Consequently, we provide an answer to the open question proposed by D. Bennis
and M. El Hajoui [3].
