If you are not offered the job, they will probably not take up your references. Even if you are shortlisted for interview, they still may not take up references until an offer is made. That way, they only have to ask for ( probably) 3 references. If there is a short list of 6, they might have to get and check 18 references, if they do all that before the interviews.
So not much need to worry about your present employers getting annoyed at finding out you want to change jobs.