On page $132$ of Fraenkel's Abstract Set Theory ($1961$), Fraenkel writes, concerning the question whether every set can be well-ordered, that
... one can prove without the axiom of choice that, to a given set $S$ and a certain way of reduction, there exists the set $M$ whose members are all possible orders M of $S$ in the way adopted. Yet this result , far-reaching as it is, does not answer the above question whether every set can be ordered, for without the axiom of choice it cannot be proved that $M≠\emptyset$, i.e. that there exists an order $M$.
Can anyone please reference me to a source which proves that for any set $S$ there exists the set $M$ whose members are all possible orders of $S$, or provide the proof?