  We study the behaviour of R\'enyi entropies in a generic thermodynamic
macrostate of an integrable model. In the standard quench action approach to
quench dynamics, the R\'enyi entropies may be derived from the overlaps of the
initial state with Bethe eigenstates. These overlaps fix the driving term in
the thermodynamic Bethe ansatz (TBA) formalism. We show that this driving term
can be also reconstructed starting from the macrostate's particle densities. We
then compute explicitly the stationary R\'enyi entropies after the quench from
the dimer and the tilted N\'eel state in XXZ spin chains. For the former state
we employ the overlap TBA approach, while for the latter we reconstruct the
driving terms from the macrostate. We discuss in full details the limits that
can be analytically handled and we use numerical simulations to check our
results against the large time limit of the entanglement entropies.
