Abstract : We show that current microlensing and dynamical observations of the Galaxy permit to set interesting constraints on the Dark Matter local density and profile slope towards the galactic centre. Assuming state-of-the-art models for the distribution of baryons in the Galaxy, we find that the most commonly discussed Dark Matter profiles (viz. Navarro-Frenk-White and Einasto) are consistent with microlensing and dynamical observations, while extreme adiabatically compressed profiles are robustly ruled out. When a baryonic model that also includes a description of the gas is adopted, our analysis provides a determination of the local Dark Matter density, ρ0 = 0.20-0.56 GeV/cm3 at 1σ, that is found to be compatible with estimates in the literature based on different techniques.