The next generation of large aperture ground based telescopes will offer the opportunity to perform accurate stellar photometry in very crowded fields. This future capability will allow one to study in detail the stellar population in distant galaxies. In this paper we explore the effect of photometric errors on the stellar metallicity distribution derived from the color distribution of the Red Giant Branch stars in the central regions of galaxies at the distance of the Virgo cluster. We focus on the analysis of the Color-Magnitude Diagrams at different radii in a typical giant Elliptical galaxy obtained from synthetic data constructed to exemplify observations of the European Extremely Large Telescope. The simulations adopt the specifications of the first light high resolution imager MICADO and the expected performance of the Multi-Conjugate Adaptive Optics Module MAORY. We find that the foreseen photometric accuracy allows us to recover the shape of the metallicity distribution with a resolution $lesssim 0.4$ dex in the inner regions ($mu_{rm B}$ = 20.5 mag arcsec$^{-2}$) and $simeq 0.2$ dex in regions with $mu_{rm B}$ = 21.6 mag arcsec$^{-2}$, that corresponds to approximately half of the effective radius for a typical giant elliptical in Virgo. At the effective radius ($mu_{rm B} simeq 23$ mag arcsec$^{-2}$), the metallicity distribution is recovered with a resolution of $simeq 0.1$ dex. It will thus be possible to study in detail the metallicity gradient of the stellar population over (almost) the whole extension of galaxies in Virgo. We also evaluate the impact of moderate degradations of the Point Spread Function from the assumed optimal conditions and find similar results, showing that this science case is robust.
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