Let $k$ be a commutative ring, and consider the category of associative non-positive DG-algebras over $k$ (thus, $A^i = 0$ for $i>0$, and the differential has degree $+1$).
Is there a closed model structure on this category with functorial cofibrant replacement, such that the weak equivalences are the quasi-isomorphisms and such that every cofibrant object is flat over $k$?