  We study the production of a forward $J/\psi$ meson and a backward jet with a
large rapidity separation at the LHC using the BFKL formalism. We compare the
predictions given by the Non Relativistic QCD (NRQCD) approach to charmonium
prediction and by the Color Evaporation Model. In NRQCD, we find that the $^3
S_1^{\, 8}$ part of the onium wavefunction is completely dominating the
process. NRQCD and the color evaporation model give similar results, although a
discrepancy seems to appear as the value of the transverse momenta of the
charmonium and of the jet decrease.
