  The exclusive vector meson production in electron-ion collisions for the
energies of the future colliders is investigated. We present predictions for
the coherent and incoherent $\phi$ and $J/\psi$ production in $eAu$ collisions
considering the possible states of nucleon configurations in the nuclear wave
function and taking into account of the non-linear corrections to the QCD
dynamics. The cross sections and transverse momentum distributions are
estimated assuming the energies of the Electron-Ion Collider (EIC), Large
Hadron Electron Collider (LHeC) and Future Circular Collider (FCC-$eh$). Our
results indicate that a future experimental analysis of these processes can
shed light on the modeling of the gluon saturation effects and constrain the
description of the QCD dynamics at high energies.
