Let us say that two sets $A$ and $B$ are comparable if there is an injection from $A$ to $B$ or there is an injection from $B$ to $A$. Obviously, in a model of ${\rm ZFC}$ any two sets are comparable by comparing their cardinalities. But this is not necessarily the case in a model of ${\rm ZF}$. For example in Cohen's classical symmetric submodel showing the independence of the Axiom of Choice from ${\rm ZF}$, there is a set of reals which is incomparable with $\omega$.

Is there a known construction of a model of ${\rm ZF}$ in which the reals are not well-ordered, but any two sets of reals are comparable?