Help: Company contacts current employer before hiring?

My current job is OK; however, I am very interested in a position posted by
another company, which is a very good fit for me. I want to apply for that
position. However, I don't want my current employer to know before I am
clear about my new job application.

Question: based on your experience, will the future company contact the
current employer for their hiring decision? If so, what is you suggestion
to avoid that in addition to mentioning "reference available upon request"?

Thank you very much for advice!