The formation of giant planets around low-mass stars remains a major challenge for planet formation theory. At the same time, observations suggest that such objects exist, even if their occurrence rates are low. Given the limited material available in disks around such stars, most existing models have difficulties to explain the origin of these planets. Standard formation models often require high disk metallicities or extended disk lifetimes. Recently, it has been shown that giant planets around low-mass stars tend to be less metal-rich than their counterparts hosted by FGK stars, which also needs to be explained by formation models. In this work we investigate the conditions required to form giant planets around low-mass stars. We employ MESA stellar evolution code, adapted to model the planetary growth and early evolution in a self-consistent framework where the accretion of solids is computed from an evolving disk featuring substructures, and the atmospheric enrichment through ablation and mixing of accreted material is included. This allows us to identify the required formation conditions and to predict their bulk compositions and internal structures.