The amount of scientific data to be transmitted from deep-space probes is very limited due to radio-frequency (RF) communications constraints. Free-space optical communication can alleviate this bottleneck, increasing data rate while reducing weight, mass, and power of communication onboard equipment. Nevertheless, optimizing the power delivery from the spacecraft to Earth is needed. In RF communications, the strategy has been to increase the aperture of ground terminals. Free-space optical communications can also follow it, as they share the limitation of low power received on Earth. As the cost of big telescopes increases exponentially with aperture, new ideas are required to maximize the aperture-to-cost ratio. This paper explores the feasibility of using the telescopes of the future Cherenkov Telescope Array as optical communication ground stations. Ground-based gamma-ray astronomy has the same power limitation; hence, Cherenkov telescopes are designed to maximize the receiver's aperture with minimum cost and some relaxed requirements. Both the critical issues of the reutilization and possible adaptations of the telescopes to optimize them for communications, as well as telescope simulations and numerical computations of several link budgets applied to worst-case scenarios, are discussed, concluding that the proposal is technically feasible and would bring important cost reductions and performance improvements compared with current designs for deep-space optical ground stations.