  The vector meson production in coherent hadron-hadron interactions at LHC
energies is studied assuming that the color singlet $t$-channel exchange
carries large momentum transfer. We consider the non-forward solution of the
BFKL equation at high energy and large momentum transfer and estimate the
rapidity distribution and total cross section for the process $h_1 h_2 \to h_1
J/\Psi X$, where $h_i$ can be a proton or a nucleus. We predict large rates,
which implies that the experimental identification can be feasible at the LHC.
