I found this overview which in the abstract talks about "effective quantization of entropy" in loop quantum gravity. As entropy is a variable depending statistically on the number of microstates in a given macrostate, it is obvious that the term "quantization" can be only effectively used.
In section V they explore with a computer the number of states that would define the entropy and find :
What one notes is that the entropy has a completely different behavior for this particular choice of interval: Instead of oscillations, the entropy seems to increase in discrete steps. Furthermore, the height of the steps seems to approach a constant value as the area of the horizon grows, thus implementing in a rather subtle way the conjecture by Bekenstein that entropy should be equidistant for large black holes. Quite remarkably, this result is robust, namely, it is independent of the counting.
It goes on to analyze further and show enhancements on the black hole area that can explain the behavior.
So it is an effective quantization of entropy, a statistical result of the quantization behavior of the area under consideration.