Large-scale commercial implementation of CO2 storage is considered a necessary mitigation strategy in most future emission scenarios. Safe storage sites at the required scales are found in the subsurface, where CO2 is injected through wells into, e.g., depleted oil and gas reservoirs for long term storage. Due to regulatory, operational, and economical constraints, pressure build-up during injection can be a limiting factor for the maximal possible injection rate and hence for the quality of a storage site. Thus, it is of both theoretical and practical interest to accurately model well pressures when conducting simulations of potential CO2 storage sites. These simulations typically employ some formulation of multiphase flow in porous media and suited numerical discretization methods. To accurately capture the singular character of the pressure gradients in proximity to wells, near-well models, such as the Peaceman well model, its various extensions, or local grid refinement around the wells, are employed. These techniques have different limitations, as the former approaches are only accurate in simplified flow regimes, while the latter can be computationally expensive. Here, we introduce a proof-of-concept for a hybrid modeling approach that addresses these challenges by integrating a machine learned near-well model into the open-source reservoir simulator OPM. The key idea is to obtain a data-driven inflow-performance relation by conducting fine-scale ensemble simulations of the near-well region. A neural network is then trained on the data and integrated into OPM. The method offers both high fidelity to fine-scale results and fast inference in large-scale simulations. This lays the groundwork for a fast, accurate and versatile approach to near-well modeling.