I see this all the time in job applications, including for the current employer section. Does it hurt your chances when you tell them not to contact them? I can understand that for former employees it'll signify that "I got fired" or "I torched bridges". I don't want my current employer to know I am trying to find another job because I am unsure of their response. I usually have the feeling it will most likely be "clean your desk out by 5pm, see ya" if they did find out. I just don't want to endanger my current position until I can find another.