Boooooooo if this happens. After being second-in-command for so long (and getting a fraction of the recognition for any success Klopp's teams have), I think it's not unnatural if he would want to move.
If he did go to another club to be a fully-fledged manager, I bet his setup and tactics and ideas about football are near enough identical to what we play under Klopp. It would be like a clone. Hopefully, if he does move, then his impact on our team, and his own ability, is overstated.