V.P. Goncalves, F.S. Navarra and D. Spiering Diffractive $\rho$ production at small x in future Electron-Ion Colliders Abstract In this paper we complement previous studies of exclusive processes in future electron-ion (eA) colliders presenting a comprehensive analysis of diffractive ρ production at small x. We compute the coherent and incoherent cross sections using on the color dipole approach, taking into account non linear QCD dynamical effects and considering different models for the dipole - proton scattering amplitude and for the vector meson wave function. The dependencies of the cross sections with the energy, photon virtuality, nuclear mass number and squared momentum transfer are analysed in detail. Moreover, we compare the non linear predictions with those obtained in the linear regime. Finally, the predictions for ρ production are compared with those for other exclusive final states. Our results demonstrate that the analysis of diffractive ρ production in future electron - ion colliders will be important to understand the nonlinear QCD dynamics. LU TP 15-47