The characterization of planetary atmospheres is a daunting task, pushing current observing facilities to their limits. The next generation of high-resolution spectrographs mounted on large telescopes - such as ESPRESSO@VLT and HIRES@ELT - will allow us to probe and characterize exoplanetary atmospheres in greater detail than possible to this point. We present a method that permits the recovery of the colour-dependent reflectivity of exoplanets from high-resolution spectroscopic observations. Determining the wavelength-dependent albedo will provide insight into the chemical properties and weather of the exoplanet atmospheres. For this work, we simulated ESPRESSO@VLT and HIRES@ELT high-resolution observations of known planetary systems with several albedo configurations. We demonstrate how the cross-correlation technique applied to these simulated observations can be used to successfully recover the geometric albedo of exoplanets over a range of wavelengths. In all cases, we were able to recover the wavelength-dependent albedo of the simulated exoplanets and distinguish between several atmospheric models representing different atmospheric configurations. In brief, we demonstrate that the cross-correlation technique allows for the recovery of exoplanetary albedo functions from optical observations with the next generation of high-resolution spectrographs that will be mounted on large telescopes with reasonable exposure times. Its recovery will permit the characterization of exoplanetary atmospheres in terms of composition and dynamics and consolidates the cross-correlation technique as a powerful tool for exoplanet characterization.