Before your interview, make sure you have your references prepared just in case the interviewer requests them. If you don't feel comfortable using your current employer as a reference, explain that you have other references better suited at this time. Those can be past supervisors.
"I am happy to provide you with a reference from my previous supervisor. Should the offer stage be reached, my current employer will be a reference. In the meantime, if you wish, I can provide you with a current client or character reference."
"Certainly! When we get to that point in the interview process, I will be delighted to have you reach out to my professional references."
"My director is aware that I am seeking a new role due to the recent company acquisition. I will include a few references to you via email which you are more than welcome to contact."
"I will be happy to provide you with any references you'd like and of course, can connect you with my current manager once I have a job offer in hand, contingent on references. Until that point, I'd prefer they don't know that I'm looking. I have some clients with whom I worked as a freelancer, so I'm happy to connect you with them at any point."
"This is so tricky, seeing as my current employer would be the absolute best reference for me, but I cannot yet let them know I am leaving. That said, I have many managers who have left the company who would happily provide a reference. Upon an offer, I would happily provide my current manager and store manager as references to my quality of work and character."
"I have some references, but I would not be comfortable with you contacting my current boss, seeing as they do not know I am looking for a new position. My previous manager has since left the company, and I would be happy to provide his information, as well as some other helpful references."
"My current Principal encouraged me to apply to your school once he knew that my family was looking to relocate I have brought a letter of reference from him. In the letter, he encourages a phone call from you should you have further questions."