May I contact your present employer for a reference?
If you’re trying to keep your job search private, this is the last thing you want. But if you don’t cooperate, won’t you seem as if you’re trying to hide something?
BEST ANSWER: Express your concern that you’d like to keep your job search private, but that in time, it will be perfectly okay.
Example: “My present employer is not aware of my job search and, for obvious reasons; I’d prefer to keep it that way. I’d be most appreciative if we kept our discussion confidential right now. Of course, when we both agree the time is right, then by all means you should contact them. I’m very proud of my record there.