Affordances are directly perceived environmental possibilities for action. Born within ecological psychology, they have been proposed to be one of the main building blocks to explain cognition from and embodied and situated perspective. Despite the interest, a formal definition of affordances in information theory terms that would allow to exploit their full potential in models of cognitive systems is still missing. We explore the challenge of quantifying affordances by using information-theoretical measures. Specifically, we propose that empowerment (i.e., information quantifying how much influence and control an agent has over the environment it can perceive) can be used to formally capture information about the possibilities for action (the range of possible behaviors of the agent in a given environment), which in some cases can constitute affordances. We test this idea in a minimal model reproducing some aspects of a classical example of body-scaled affordances: an agent passing through an aperture. We use empowerment measures to characterize the affordance of passing through the aperture. We find out that empowerment measures yield a similar transition to the one found in experimental data in humans in the specialized literature on ecological psychology. The exercise points to some limitations for formalizing affordances and allows us to pose questions regarding how affordances can be differentiated from more generic possibilities for action.