Blazars are active galactic nuclei (AGN) with a relativistic jet oriented toward the observer. This jet is composed of accelerated particles which can display emission over the entire electromagnetic spectrum. Spectral variability has been observed on short- and long-time scales in AGN, with a power spectral density (PSD) that can show a break at frequencies below the well-known red-noise process. This break frequency in the PSD has been observed in X-rays to scale with the accretion regime and the mass of the central black hole. It is expected that a break could also be seen in the very-high-energy gamma rays, but constraining the shape of the PSD in these wavelengths has not been possible with the current instruments. The Cherenkov Telescope Array (CTA) will be more sensitive by a factor of five to ten depending on energy than the current generation of imaging atmospheric Cherenkov telescopes, therefore it will be possible with CTA to reconstruct the PSD with a high accuracy, bringing new information about AGN variability. In this work, we focus on the AGN long-term monitoring program planned with CTA. The program is proposed to begin with early-start observing campaigns with CTA precursors. This would allow us to probe longer time scales on the AGN PSD.