A firm may contact your current employer during verification, but you should not assume it will do so before you authorize the process.

Reference and background-check procedures vary by office and jurisdiction, particularly for people who are still employed.

If confidentiality is important, a recruiter can often explain when checks occur and whether alternative references are possible. Confirm the point in the hiring process when references might be requested, and document any confidentiality preference.

Treat your search as confidential and ask recruiting when references or background checks are performed. You can request that your employer not be approached without your knowledge, but get the process clarified before providing contact details.

This is the part of applying while employed that concerns me most.