Atmospheric composition provides essential markers of the most fundamental properties of giant exoplanets, such as their formation mechanism or internal structure. New-generation exoplanet imagers, like VLT/SPHERE or Gemini/GPI, have been designed to achieve very high contrast (>15 mag) at small angular separations ($<$0.5\as) for the detection of young giant planets in the near-infrared, but they only provide very low spectral resolutions ($R<100$) for their characterization. High-dispersion spectroscopy at resolutions up to $10^5$ is one of the most promising pathways for the detailed characterization of exoplanets, but it is currently out of reach for most directly imaged exoplanets because current high-dispersion spectrographs in the near-infrared lack coronagraphs to attenuate the stellar signal and the spatial resolution necessary to resolve the planet. Project HiRISE (High-Resolution Imaging and Spectroscopy of Exoplanets) ambitions to develop a demonstrator that will combine the capabilities of two flagship instruments installed on the ESO Very Large Telescope, the high-contrast exoplanet imager SPHERE and the high-resolution spectrograph CRIRES+, with the goal of answering fundamental questions on the formation, composition and evolution of young planets. In this work, we will present the project, the first set of realistic simulations and the preliminary design of the fiber injection unit that will be implemented in SPHERE.