The first heavy fermion superconductor CeCu2Si2 is still only partially understood. At high pressures, superconductivity is supposed to be mediated by a different mechanism than at ambient pressure, where spin fluctuations most likely act as pairing glue. We have obtained and analyzed new resistivity data up to 7GPa on a good quality CeCu2Si2 single crystal with an unprecedented high transition temperature. For the first time, we establish quantitatively that CeCu2Si2 lies in proximity to a valence transition: the critical end point could be located at 4.5±0.2GPa and a slightly negative temperature, and the corresponding valence cross-over line has been added to the p-T phase diagram. This outcome is essential for the theoretically predicted critical valence fluctuations scenario, and opens new routes for further investigations in other Ce-based compounds.